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REDISTRIBUTION WITH GROWTH Hollis Chenery, Montek S. Ahluwalia, C. L. G. Bell, John H. Duloy, and Richard Jolly "A major contribution to the literature of income distribution in less developed countries." -Journal of DevelopingAreas "A rich and instructive contribution for anyone teaching economic development and the complex relations between distribution and growth." -Political Science Quarterly "Exceptionally valuable analysis of development policies . . . Redistributionwith Growth,a model handbook for planners, is also an extremely useful guide to the state of the discipline of development economics." -Journal of Economic Literature 324 pages.Figures, tables, bibliography. Availablein clothand papereditions.

INCOME INEQUALITY AND POVERTY: METHODS OF ESTIMATION AND POLICY APPLICATIONS Nanak Kakwani New techniques, derived from actual data, analyze problems of size distribution of income and evaluate alternative fiscal policies. Both ethical evaluation and statistical measurement are considered. The author systematizes existing knowledge and introduces a number of new findings. About 320pages. Figures, bibliography. Availablein clothedition. Growth with Equity THE TAIWAN CASE

A World Bank Research Publication

Growth with Equity THE TAIWAN CASE

John C. H. Fei Gustav Ranis Shirley W. Y. Kuo with the assistance of Yu-Yuan Bian Julia Chang Collins

Published for the World Bank Oxford University Press Oxford UTniversityPress

NEW YORK OXFORD LONDON GLASGOW TORONTO MELBOURNE WELLINGTON HONG KONG TOKYO KUALA LUMPUR SINGAPORE JAKARTA DELHI BOMBAY CALCUTTA MADRAS KARACHI NAIROBI DAR ES SALAAM CAPE TOWN (© 1979 by the International Bank for Reconstruction and Development / The World Bank 1818 H Street, N.W., Washington, D.C. 20433 U.S.A. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior permission of Oxford University Press. Manufactured in the United States of America. The views and interpretations in this book are the authors' and should not be attributed to the World Bank, to its affiliated organizations, or to any individual acting in their behalf.

Library of Congress Cataloging in Publication Data Fei, John C. H. Growth with equity Includes bibliographical references and index. 1. Income distribution-Taiwan. 2. Taiwan- Economic conditions. I. Ranis, Gustav, joint author. II. Kuo, Shirley W. Y., 1930- joint author. III. Title. HC430.5.Z915196 339.2'0951'249 79-23354 ISBN 0-19-520115-9 ISBN 0-19-520116-7 pbk. Foreword

CAN GOVERNMENTS MODIFY POLICIES to produce a more equitable distribution of the benefits of economic growth? Or must they initiate more drastic structural changes? These questions are at the heart of one of the most debated issues in economic development. Most studies of developing countries indeed show that the rich tend to benefit more than the poor from rises in national income during the early phases of economic growth. The experience of Taiwan thus is of particular interest, because the country has managed to achieve rapid growth with considerable equity. This study by Fei, Ranis, and Kuo develops an analytical framework that relates changes in family income to the evolution of its several components, which are in turn related to development theory. Application of this method to Taiwan helps to explain the observed changes in income distribution during two decades of rapid growth. Circumstances specific to Taiwan naturally played an important part in this performance. But in speculating about the effects of government intervention and the pattern of growth on changes in equity, the authors identify processes that are relevant both to economic theory and to economic policy. The authors' catalog of findings deserves consideration by pessimists who feel the tradeoff between growth and equity to be inevitable. This book is one of a series of studies investigating the relations between growth and distribution in the developing countries-a series supported by the research program of the World Bank. Other books in this series include Income Distribution Policy in Developing Coun- tries: A Case Study of Korea by Irma Adelman and Sherman Robinson, Public Expenditure in Malaysia: Who Benefits and Why by Jacob Meerman, Who Benefits from Government Expenditure: A Case Study

v Vi FOREWORD of Colombia by Marcelo Selowsky, and Redistribution with Growth by Hollis Chenery and others. Additional titles forthcoming at this writing include Models of Growth and Distribution for Brazil by Lance Taylor and others, Urban Labor Markets and Income Distribution in Malaysia by Dipak Mazumdar, and Inequality and Poverty in Malay- sia: Measurement and Decomposition by Sudhir Anand. As in these other studies, the authors of this book alone are responsible for the findings. It is the Bank's hope that this series will improve understanding of the choices that developing countries have with respect to growth and the distribution of income. Clearly, the method of analysis and findings for Taiwan presented here are important contributions to that understanding.

HOLLIs B. CHENERY Vice President, Development Policy The World Bank Contents

Preface xviii

INTRODUCTION. An Approach to Growth with Equity 1 Framework of Analysis S Problems of Measurement 6 Problems of Data 10

PART ONE. THE CASE OF TAIWAN 17 1. Historical Perspective 21 The Colonial Legacy 26 Primary Import Substitution, 1953-61 30 Export Substitution, 1961-72 21 2. Economic Growth and Income Distribution, 1953-64 37 Land Reform 38 Agricultural Development during the 1950s 46 The Distribution of Assets and Industrial Growth 50 Effects of Growth on Equity 54 3. Growth and the Family Distribution of Income by Factor Components 72 Income Inequality and Its Factor Components 75 Growth and the Distribution of Income 83 Empirical Application to Taiwan 90 Impact of Growth on FID: Quantitative Aspects 99 Impact of Growth on FID: Qualitative Aspects 108 Summary and Conclusions 127 4. The Inequality of Family Wage Income 1SO Empirical Data 182 Analytical Framework 188

vii viii CONTENTS

Labor Heterogeneity and the Wage Rate: First-level Analysis 141 Inequality of Income of Individual Wage Earners: Second-level Analysis 146 Inequality of Family Wage Income: Third-level Analysis 168 Conclusion 193 Appendix 4.1. Data on the Distribution of Family Income in Taiwan 193 Appendix 4.2. Linear Regression and the Model of Additive Factor Components 203 5. Income Distribution and Economic Structure 224 The Decomposition Equation 226 Empirical Decomposition by Sectors and Homogeneous Groups 231 Changes in Income Inequality Associated with Industrialization and Urbanization 243 Additional Reflections 249 6. Taxation and the Inequality of Income and Expenditure 264 Statistical Data 267 Analytical Framework 270 Decomposition of Family Income after Tax 272 The Impact of Taxation on Income Inequality 279 Future Research 289 Appendix 6.1. Estimation of Indirect Tax 293 7. Relevance of Findings for Policy 308 The Inequality of Family Income 312 The Inequality of Family Wage Income 317 The Inequality of Taxation and Expenditure 321 Future Research 323

PART Two. THE METHODOLOGY OF GINI COEFFICIENT ANALYSIS 325 8. Basic Concepts 328 Definition of the Gini Coefficient 328 The Gini Coefficient as Related to the Rank Index of Y 330 The Gini Coefficient as the Average Fractional Gap 331 The Pseudo Gini Coefficient 334 9. Testing Hypotheses 338 Testing Hypotheses by Supporting and Contradicting Gaps 340 Gini Decomposition for Hypothesis Testing 342 Net Supporting Gap 343 CONTENTS

Graphic Summary of the Gini and Pseudo Gini Coefficients 346 Correlation Characteristics 348 10. The General and Special Models of Additive Factor Components 351 Decomposition of G, into Pseudo Factor Ginis 352 Exact Decompositionof G, into Factor Ginis 357 ComputationProcedure for Exact Decomposition 359 The Gini Coefficientunder Linear Transformation 361 Linear Model of Additive Factor Components 363 Monotonic Model of Additive Factor Components 365 Linear Approximation of Factor Components 367 Linearity Error 369 Approximation of the Monotonic Model 370 11. Applications and Extensions of the Models of Decomposition 373 Remarks on Chapter Three 374 Renmarkson ChapterSix 375 Additive Factor Componentsand GrowthTheory 376 Income Componentswith ObservationError 378 Family Income with NegativeComponents 380 Computation Procedure 383 12. Regression Analysis, Homogeneous Groups, and Aggregation Error 386 RegressionAnalysis 386 Family Income Inequality with HomogeneousGroups 394 Gini Error Arising from the Use of GroupedData 403 GroupingError in the Analysis of Additive Factor Components 405 Index 411

Figures

1.1. Ratios of Imports of NondurableConsumer Goods to Total Importsand Total Supply, 1953-72 27 1.2. GrowthRate of Real Gross National Product per Capita, 1953-72 28 1.3. Ratiosof Savingsand Investmentto GrossNational Product, 1953-72 29 1.4. Ratiosof Exportsof PrimaryGoods and IndustrialGoods to Total Exports, 1953-72 SO Z CONTENTS

1.5. Ratio of Exports to Gross National Product, 1953-72 31 1.6. Ratios of Agricultural and Nonagricultural Employment to Total Employment, 1953-72 82 1.7. Index Numbers of Real Wages of Males and Females in Manufacturing, 1953-72 S3 1.8. Index Numbers of Real Wages of Males and Females in Textiles, 1953-72 S3 1.9. Index Numbers of Real Wages of Males and Females in Transport and Communications, 1953-72 34 1.10. Gini Coefficients,1953-72 35

3.1. Gini Coefficientsof Total and Factor Incomes, by Model, 1964-72 91 3.2. Factor Shares, by Model, 1964-72 96 3.3. Gini Coefficientsof Total Income, by Model, 1964-72 100 3.4. Gini Coefficientsof Wage and Property Income, by Model, 1964-72 101 3.5. Ratio of the Wage Share in Nonagricultural Production to the Property Share, by Model, 1964-72 117 3.6. Ratio of Average Urban Income to Average Rural Income for Wage and Property Income, 1964-72 118 3.7. Ratio of the Total Income Share of the Top 10 Percent to That of the Bottom 10 percent, by Model, 1964-72 122 3.8. Ratio of the Wage Income Share of the Top 10 Percent to That of the Bottom 10 Percent, by Model, 1964-72 123 3.9. Ratio of the Property Income Share of the Top 10 Percent to That of the Bottom 10 Percent, by Model, 1964-72 124 3.10. Ratio of the Agricultural Income Share of the Top 10 Percent to That of the Bottom 10 Percent, by Model, 1964-72 125

4.1. The Emergence of Splinter Groups 153 4.2. The Wage Gini and the Explained Portion of the Wage Gini, by Location, 1966 160 4.3. Percentage Composition of Factor Contributions, by Location, 1966 162 4.4. Composition of the Contribution of Education to Explained Inequality, by Location, 1966 163 4.5. Composition of the Contribution of Age to Explained Inequality, by Location, 1966 165 4.6. Composition of the Contribution of Sex to Explained Inequality, by Location, 1966 167 4.7. Composition of the Contribution of Family Influence to Explained Inequality, by Location, 1966 168 4.8. Contribution to Family Wage Income Inequality, by Labor Grade, 1966 176 CONTENTS xi

4.9. Inequality of Family Ownership of Labor of Different Grades, 1966 178 4.10. Correlation Characteristics between Total Family Income and Family Ownership of Labor, 1966 179 4.11. The Economic Weight of Different Grades of Labor, 1966 180 4.12. Weighted Average of the Education Gini Plotted against the Average Wage Rate, by Level of Education, 1966 182 4.13. Weighted Average of the Education Correlation Characteristic Plotted against the Average Wage Rate, by Level of Education, 1966 182 4.14. Weighted Average of the Education Weight Plotted against the Average Wage Rate, by Level of Education, 1966 183 4.15. Gini Coefficients in Four Cases, Plotted against the Wage Rate, by Level of Education 188 4.16. Correlation Characteristics in Four Cases Plotted against the Wage Rate, by Level of Education 189 4.17. Weights in Four Cases Plotted against the Wage Rate, by Level of Education 189 5.1. Income Distribution for Agricultural, Nonagricultural, and All Sectors 228 6.1. Contributions to the Inequality of Family Income after Tax, by Category of Expenditure, 1964-73 272 6.2. Correlation Terms for the Decomposition of Family Income after Tax, by Category of Expenditure, 1964-73 27S 6.3. Shares for the Decomposition of Family Income after Tax, by Category of Expenditure, 1964-73 276 6.4. Gini Coefficients for the Decomposition of Family Income after Tax, by Category of Expenditure, 1964-73 277 6.5. Flows of Income before Tax to Taxes and Income after Tax, by Family 282 6.6. Contributions to the Inequality of the Tax Burden, 1964-73 284 6.7. Shares for the Decomposition of the Tax Burden, 1964-73 288 6.8. Gini Coefficients of Direct and Indirect Tax, 1964-73 289 8.1. The Lorenz Curve 329 8.2. The Pseudo Lorenz Curve 335 8.3. The Pseudo Lorenz Curve for an Inverse Wage Pattern 337 9.1. Iso Gini Coefficient Contour Lines 347 12.1. Behavior of Indexes of Inequality under Different Levels of Aggregation 408 Xii CONTENTS

Tables

1.1. Distribution of Land and Owner-Cultivator Households, by Size of Holding, 1920, 1932, and 1939 28 1.2. Distribution of Farm Families and Agricultural Land, by Type of Cultivator, 1920-22, 1927-30, and 1939-40 24 2.1. Area and Households Affected by Land Reform, by Type of Reform 41 2.2. Distribution of Land and Owner-Cultivator Households, by Size of Holding, 1952 and 1960 42 2.3. Distribution of Farm Families and Agricultural Land, by Type of Cultivator, 1948-60 48 2.4. Distribution of Agricultural Income, by Factor, 1941-56 44 2.5. Parameters and Indexes of Agricultural Employment, Production, and Development, 1952-64 46 2.6. Distribution of Industrial Production, by Public and Private Ownership, 1952-64 51 2.7. Gini Decomposition Analysis Based on Farm Family Income Stratified by Size of Farm, 1952-67 55 2.8. Multiple Cropping, by Size of Farm, 1952 and 1967 56 2.9. Average Income of Farm Families, by Size of Farm, 1952-67 58 2.10. Distribution of Factor Shares, by Size of Farm, 1952-67 59 2.11. Distribution of Farm Households, Income, and Factor Shares, by Size of Farm, 1952-67 60 2.12. Off-farm Activity of Farm Families, by Size of Farm, 1960 61 2.13. Composition of Off-farm Employment of "Moved-out" Workers, by Type of Work, 1963 62 2.14. Establishments in Taiwan, by Location, 1951 and 1961 63 2.15. Gini Coefficients and Factor Shares Based on Income of Urban Wage and Salary Workers, 1955 and 1959 64 2.16. Measures of the Equity of the Family Distribution of Income, 1953, 1959, and 1964 66 2.17. Distribution of National Income, by Factor Shares, 1951-72 68 2.18. Gross Domestic Product, Employment, Share of Wages in Value Added, and Labor Intensity, by Industry, Various Years 70 3.1. Numerical Example with Three Factor Income Components and with Total Income Arranged in a Monotonically Nondecreasing Order 76 3.2. Gini Decomposition by Additive Factor Components, 1964-72 92 3.3. Regression Results for Decile Income Groups, 1964-72 94 CONTENTS xiii

3.4. Comparison of Factor Shares from National Accounts and Household Surveys, 1952-72 97 3.5. Changes in the Family Distribution of Income and Their Decomposition, All-households Model, 1964-72 102 3.6. Changes in the Family Distribution of Income and Their Decomposition, Rural-households Model, 1966-72 104 3.7. Changes in the Family Distribution of Income and Their Decomposition, Urban-households Model, 1966-72 106 3.8. Gini Coefficients Based on Decile Population Groups for Urban, Semiurban, and Rural Households, 1964 and 1968 111 3.9. Establishments in Taiwan, by Location, 1951-71 116 3.10. Capital Intensity, by Region and Sector, 1961 and 1971 119 4.1. Relative Wage Rates and Frequency Distribution of Labor, by Education, Sex, and Job Location, 1966 134 4.2. Relative Wage Rates and Frequency Distribution of Labor, by Age, Sex, and Job Location, 1966 135 4.3. Wage Parity of Female Workers, by Age and Education, 1966 136 4.4. Numerical Example Corresponding to the Gross-listing of Information on the Wage Rate and Frequency Distribution of Workers in Tables 4.20-4.27, by Sex and Level of Education 140 4.5. Numerical Example Classifying Workers into Five Families and Tracing Wage Income Components to the Membership Composition of Those Families 141 4.6. Regression Coefficients of Four Explanatory Variables, by Job Location, 1966 148 4.7. Influence of Total Family Income on Wage Rates, by Sex and Age, 1966 144 4.8. Distribution of Families, by Job Location and Total Family Income, 1966 145 4.9. Numerical Example of Regression Analysis for Five Wage Earners and Two Explanatory Variables 148 4.10. Numerical Example of the Formation of New Homogeneous Groups with Eight Workers 151 4.11. Numerical Example of the Gap between the Relative Value of the Education Characteristic for a Privileged Group and That for a Less Privileged Group 154 4.12. Decomposition Analysis of the Inequality of the Wage Rate, by Location and Labor Characteristic, 1966 159 4.13. Wage Rates, Family Membership Ginis, and Other Variables for Thirty-seven Categories of Workers, 1966 172 4.14. The Inequality of Wage Income: Numerical Example of Uniform Family Size and Homogeneous Family Composition 184 4.15. The Inequality of Wage Income: Numerical Example of Uniform Family Size and Semihomogeneous Family Composition 187 xiV CONTENTS

4.16. The Inequality of Wage Income: Two Numerical Examples of Nonuniform Family Size and Homogeneous Family Composition 191 4.17. The Inequality of Wage Income: Two Numerical Examples of Descending Family Size and Homogeneous Family Composition 192 4.18. Size of Sample for DGBAS Surveys, 1964-73 194 4.19. Coding for Characteristics of Individual Wage Earners and Income-earning Families 200 4.20. Annual Wage Rates of Female Workers, by Age, Occupation, Job Location, and Level of Education, 1966 204 4.21. Annual Wage Rates of Male Workers, by Age, Occupation, Job Location, and Level of Education, 1966 206 4.22. Number of Female Workers, by Age, Occupation, Job Location, and Level of Education, 1966 208 4.23. Number of Male Workers, by Age, Occupation, Job Location, and Level of Education, 1966 212 4.24. Number of Rural Workers and Average Annual Wage Rate, by Education, Sex, and Age, 1966 216 4.25. Number of Town Workers and Their Annual Wage Rate, by Education, Sex, and Age, 1966 218 4.26. Number of City Workers and Their Annual Wage Rate, by Education, Sex, and Age, 1966 220 4.27. Number of Workers and Average Annual Wage Rate, by Education, Sex, and Age, 1966 222 5.1. Numerical Example of Income Distribution for Agricultural, Nonagricultural, and All Sectors 229 5.2. Decomposition Analysis, by Farm and Nonfarm Sectors, 1964-72 282 5.3. Decomposition Analysis, by Degree of Urbanization in the Six-sector Classification, 1966 and 1972 286 5.4. Decomposition Analysis, by Degree of Urbanization in the Three-sector Classification, 1966 and 1972 287 5.5. Decomposition Analysis, by Age of Head of Family, 1964 and 1972 2S8 5.6. Decomposition Analysis, by Sex of Head of Family, 1964 and 1972 289 5.7. Decomposition Analysis, by Number of Persons Employed in Family, 1964 and 1972 240 5.8. Decomposition Analysis, by Educational Level of Head of Family, 1972 242 5.9. Income Disparities, by Farm and Nonfarm Families, 1964 and 1972 244 CONTENTS xV

5.10. Income Disparities, by Degree of UJrbanization in the Six-sector Classification, 1966 and 1972 244 5.11. Income Disparities, by Degree of Urbanization in the Three-sector Classification, 1966 and 1972 245 5.12. Causes of the Reduction in Income Inequality, by Farm and Nonfarm Sectors, 1964-72 246 5.13. Causes of the Reduction in Income Inequality, by Degree of Urbanization in the Six-sector Classification, 1966-72 247 5.14. Causes of the Reduction in Income Inequality, by Degree of Urbanization in the Three-sector Classification, 1966-72 248 5.15. Sources of Income of Farm and Nonfarm Families, by Decile, 1966 and 1975 250 5.16. Growth of Income of Farm and Nonfarm Families, by Decile, 1966-75 251 5.17. Gini Index of Land Concentration in Selected Countries, Comparisons for Various Years 252 5.18. Indexes of the Productivity of Land and Labor in Agriculture, Taiwan, 1950 and 1955 253 5.19. Relative Tax Burden of Farm and Nonfarm Families, by Income Range, 1966 and 1975 254 5.20. Average Size of Families, by Income Bracket, 1966 and 1972 256 5.21. Average Size of Farm Families, by Income Bracket, 1966 and 1972 257 5.22. Average Size of Nonfarm Families, by Income Bracket, 1966 and 1972 258 5.23. Income Disparities, by Size of Household, 1966 and 1972 259 5.24. Income Disparities, by Number of Persons Employed in Family, 1964 and 1972 260 5.25. Causes of the Reduction in Income Inequality, by Number of Persons Employed in Family, 1964-72 261 5.26. Income Disparities, by Age of Head of Family, 1964 and 1972 262 5.27. Causes of the Reduction in Income Inequality, by Age of Head of Family, 1964-72 262 5.28. Income Disparities, by Sex of Head of Family, 1964 and 1972 263 5.29. Causes of the Reduction in Income Inequality, by Sex of Head of Family, 1964-72 263 6.1. Categories of Household Expenditure and Their Indirect Tax Burden, 1966 268 6.2. Decomposition of the Inequality of Family Income after Tax, 1964-73 274 6.3. Decomposition of the Inequality of Family Income before Tax, 1964-73 280 XVi CONTENTS

6.4. Decomposition of the Inequality of the Tax Burden, 1964-73 286 6.5. Family Income and Expenditure, by Category and Income Class, 1964 296 6.6. Family Income and Expenditure, by Category and Income Class, 1966 298 6.7. Family Income and Expenditure, by Category and Income Class, 1968 SOO 6.8. Family Income and Expenditure, by Category and Income Class, 1970 302 6.9. Family Income and Expenditure, by Category and Income Class, 1972 304 6.10. Family Income and Expenditure, by Category and Income Class, 1973 306 9.1. Numerical Example of Income Fractions, Income Ranks, and Education Ranks for Five Families 339 10.1. Numerical Example of the Problem of Additive Factor Components 352 10.2. Gini Decomposition by Pseudo Factor Ginis, 1964-72 354 10.3. Numerical Example of Exact Decomposition of Gu into Factor Ginis 358 11.1. Numerical Example of Original Income Data 384 11.2. Distributive Shares, Gini Coefficients, and Pseudo Gini Coefficients for Original Data in Table 11.1 384 11.3. Decomposition Analysis of Original Data in Table 11.1 385 12.1. Numerical Example of Income Data and Regression Terms 391 12.2. Distributive Shares, Gini Coefficients, and Pseudo Gini Coefficients for Original Data in Table 12.1 392 12.3. Decomposition Analysis of Original Data in Table 12.1 393 12.4. Numerical Example of the Classification of Families by Education 395 12.5. Numerical Example of the Classification of Seven Families into Three Homogeneous Groups 400 12.6. Decomposition Analysis of Data in Table 12.5 401 12.7. Numerical Example of the Factor Gini Error in Grouped Data 406 CONTENTS xVii

Acronyms and Initials

ATP After the turning point BTP Before the turning point DGBAS Directorate-General of Budget, Accounting, and Statistics FID Family distribution of income GDP Gross domestic product GNP Gross national product ICCT Industrial and Commercial Census of Taiwan JCRR Joint Commission for Rural Reconstruction LDC Less developed country NDP Net domestic product OECD Organization for Economic Cooperation and Development Preface

THis VOLUME IS DEDICATED to the study of the family distribution of income in the context of growth. Because the empirical application is to Taiwan, we quote at the outset a famous observation Confucius made 2,500 years ago: "Inequality is to be lamented more than scarcity." More recently, Ricardo had this to say in a letter to Malthus: "Political economy, you think, is an enquiry into the nature and causes of wealth-I think it should be called an enquiry into the laws which determine the division of the produce of industries amongst the classes who concur in its formation." Ricardo's sentiment ushered in the classical school's interest in the social problem of income distribution. Although that interest lapsed for some time, few today will deny that the persistence of income gaps between wealthy and poor families probably is the most serious social problem and that such gaps will continue to be a serious problem as long as there is scarcity. It is curious then, despite such universal recognition of the social importance of the distribution of family income, that modern economists did not devote serious attention to it until really quite late: that is, until the post-Keynesian era after the Second World War. The classical economists focused on the functional distribution of income and attempted to explain the forces that determine the division of the national income into various functional distributive shares. The problem of the equity of income distribution is entirely different. The phenomenon is explained by the pattern of total income received by families. That pattern can be summarized by the degree of inequality of income, as measured by the Gini coefficient or some other index of inequality. The much more complicated nature of this problem, as well as the only recently reawakened interest in the fate of the poorer classes under conditions of growth, were undoubtedly

xviii PREFACE xiX

responsible for the delayed rebirth of academic and policy interest in this area. It is no coincidence that the new concern with the family distribution of income emerged, after a lag, with the revival of interest in the study of economic growth-itself a post-Keynesian, postwar phenomenon. The inequality of the distribution of family income must be traced directly to the inequality in the pattern of family ownership of the primary factors of production. These factors include physical and human assets, as well as their compensation. Because growth theory is primarily concerned with the augmentation of assets-that is, with capital formation, population growth, and the accumulation of human capital-the distributional impact of any change in the pattern of asset ownership can be meaningfully assessed only in the context of growth. The linkage between the family distribution of income and the theory of growth, and the conclusions for theory and policy which can be derived from the inductive examination of the Taiwan experience, thus constitute the focal points of this volume. We clearly have not solved the problem. Indeed we shall be pleased if it is judged that we have somewhat advanced the cause. Moreover we fully realize that tensions between the political need for action and the scientific need for a better understanding of behavior are perhaps more pronounced in the study of income distribution than in any other area of economics. In fact, researchers are likely to have to defend themselves against a two-front attack. On one front, academic and scientific progress demands the formalism of variables and equations within a deterministic theory based on behavioristic hypotheses. Such formalism is technically difficult to achieve in this field, to say the least. On the second front, action-oriented policymakers demand to know the implications of research findings with an unusually high time preference. Consequently researchers run the risks of having to navigate a narrow course between accusations of sloppy humanitarianism and those of esoteric irrelevance. We nevertheless feel that both charges can and must be met. Academics surely understand that there often exists a pretheoretical stage in the social sciences-a stage in which inductive evidence is examined to separate the relevant elements of a problem from the irrelevant, the essential from the nonessential. Because of the brief life of research examining the distribution of family income, most contemporary work cannot, we believe, escape from the grip of the pretheoretical stage we are in. The present volume is no exception. Zr PREFACE

Policymakers, on the other hand, sometimes need to be reminded that good policy is ultimately based on good theory. Although no one expects a moratorium on policy, planning commissions and aid donors have little at their disposal to permit them even to rule out absurdities. Given the many remedies proposed to cure the maldistribution of income, including fiscal reform, poverty relief, public works, and land reform, this volume's aim is to begin to fill the vacuum by specifying some of the things known about the behavioral relations, and consequently the policy relations, between growth and the distribution of income. In short, we are concerned with developing a theory relating income distribution to growth-a theory which is to be implemented with statistical data, and a theory from which policy recommendations are to be deduced. Given the pioneering nature of this area of inquiry, the task is difficult. The interpretation of results, drawn from imperfect data, suffers from the absence of a recognized standard of international comparison. For example, what is the real significance of, say, a 2 percent drop in the Gini coefficient over a ten-year period? In addition, the deduction of policy recommendations, which always is an art, is particularly difficult at an early phase when the theory still is highly imperfect. We are aware of these shortcomings, and we disclaim any notion that our methodology has been perfected or that definitive policy conclusions can be drawn from it. Our main hope is that this volume may help to open up a new approach to understanding an important social problem. We also recognize that all researchers concerned with the distribution of income face a conceptual difficulty of a basically philosophical nature. If a Gini coefficient [GQ]is used to measure the degree of inequality of a pattern of income distribution [Y = (Y,, Y2, . . ., Yn) ], the underlying implication always is that perfect equality, G, = 0 or Y, = Y2 = . .. = Y,n represents the social ideal. This implication is true for all the familiar indexes of inequality which satisfy the axiom of the desirability of transfer: the axiom that any redistribution from rich to poor increases social equity. The conceptual difficulty arises when that axiom is subject to question. Any modern industrial society, regardless of its organizational structure, requires a pyramid of positions differentiated by earning power. There should, for example, be relatively few positions for doctors and relatively many for unskilled workers. Individuals differentiated by ability, determination, and other characteristics will attempt to occupy positions in the pyramid. As a result, in any PREFACE Xxi rational society, perfect income equality among individuals cannot really prevail. Regardlessof how positions are allocated to individuals, the pyramid itself determines a nonzero value for the Gini. This probably explains why a Gini value below 0.30 is seldom found even in the most equitable society. The ideal criterion of equity should thus be the equality of opportunity to reach for various positions in the pyramid. The major obstacles in the way of such equality of opportunity are, we believe, inherent in the genealogicalrelations of the family system. Even when markets are perfect and every position is rewarded according to its productive contribution-that is, even when there are no elements of discrimination or distortion-not every member of the new generation has an equal opportunity to reach for these positions. Differences in family background are the reason. The son of a wealthy black family, for example, can be expected to earn more than the son of a poor white family. This inherent inequality of opportunity, whether caused by variations in inherited assets or educational opportunities, probably is the principal cause of individual income inequality. Thus intergenerational, occupational, or class mobility represents the ultimate test of true equity in a rational society. Income equality does not. In this volume we have chosen to study the family distribution of income as it relates to growth. The choice is based in part on the belief that a more equal distribution of income across families increases the equality of opportunity in each generation. For this reason a lower value or decline in the Gini coefficientwill be regarded as a "good thing." We admit this to be an arbitrary value judgment on our part. We are content to leave to others, more competent than we, the unresolved philosophical issues raised in this context. We would like to thank the World Bank for its financial support and Montek Ahluwalia, Clive Bell, Hollis Chenery, John Duloy, and Graham Pyatt for their substantive comments. We are most grateful for the thorough and perceptive comments of Anthony Atkinson, who acted as the Bank's outside reader. Others whose constructive criticisms were appreciated in the course of this effort include Gary Fields, Mahar Mangahas, and Guy Orcutt. We were beneficiaries of the cooperation of the Economic Planning Council of Taiwan and the Economic Growth Center at Yale. Our thanks also go to M. C. Cheng, M. M. Hsih, T. F. Hsuh, Francoise Le Gall, Regina Liu, and C. M. Tang for their help in preparing the manuscript, and to Cheryl Hunt and Paula Saddler for their patience and expert typing. Zxii PREFACE

Bruce Ross-Larson edited the manuscript for publication. Raphael Blow prepared the charts, Brian J. Svikhart managed production of the book, and Kathryn M. Tidyman indexed the text.

JOHN C. H. FEI GUSTAV RANIS SHIRLBY Kuo New Haven, Connecticut December 1979 INTRODUCTION

An Approach to Growth with Equity

THE INEQUALITY OF THE DISTRIBUTION OF INCOME AND WEALTH in a given society has been of concern to man for a very long time. Economists nevertheless have traditionally focused their attention more on the functional distribution of income and the determination of factor prices and shares in the manner of the classical and Austrian schools. Although the size or family distribution of income (FID) has not been totally neglected-witness the literature on utopian socialism and the use of the Lorenz curve-it probably is fair to say that economists have viewed FID more as a descriptive device. Until quite recently, it was not successfully integrated with the main body of analytical economics.' During the early postwar period, the main social problem everywhere, but especially in the newly independent developing world, was a concern with growth. The 1950s and 1960s have been characterized, if unfairly, as being exclusively oriented to growth. Growth was not quite a religion, but common sense led to one basic assumption: when the pie is small, policies must be geared to increasing its size, at least for the time being. The concept of redistribution could not have much meaning until the pie became much larger.

1. In the first decades of this century, such writers as Cannan and Dalton were concerned with the measurement of the size distribution of income and its integration with mainstream economics. Historical hindsight suggests, however, that their attempt at integration was not very successful. Because the size distribution of income appears to be a growth-related issue, related to the accumulation of human and physical assets, the chance for successfulintegration became real only with the revival of interest in growth after the SecondWorld War.

1 2 INTRODUCTION

In recent years, however, all parties have become increasingly unwilling to accept the "grow now, redistribute later" package. One reason for this is a growing reluctance to be generous only to future generations. But the main reason is the growing skepticism about whether "later" would ever come. Nevertheless most language in currency today still relates to redistribution. How is a better measure of equity to be regained after growth has occurred? How much growth is to be sacrificed for the sake of better distribution along the way? This second formulation comes closer to the heart of this volume, with one proviso: we do not accept the notion that there always has to be a sacrifice. Consequently it seems more appropriate to address the extent to which equity can accompany growth from the start, not to constrain the discourse to the achievement of one objective at the expense of the other. Of course, the matter may be as much semantic as it is substantive. Most economists and policymakers understandably share, at least implicitly, the assumption of the need for tradeoffs having varying degrees of severity. Consider the work of Kuznets, Paukert, and Adelman and Morris.2 On the basis of cross-country cross-sections, they seem to discern an inverse U-shaped relation between growth and equity. They conclude that, as income increases from low levels in a developing society, the distribution of income must first worsen before it can improve. Two facts support their conclusion. First, today's less developed countries (LDCS) generally have distributions which are less equal than those of the rich countries. Second, accelerated LDC growth has most often been accompanied by a worsening of already unfavorable indexes of equality. Based on the historical evidence, almost all contemporary LDCS support the general aura of tradeoff pessimism. Taiwan is one exception. According to the best data available, Taiwan's family distribution of income in the 1950s was not very different from the unfavorable levels most LDCS seem to be prey to in the early years of

2. Simon Kuznets, "Economic Growth and Income Inequality," American Economic Review, vol. 45, no. 1 (March 1955), pp. 1-28; idem, "Quantitative Aspects of the Economic Growth of Nations: VIII, Distribution of Income by Size," Economic Development and Cultural Change, vol. 11, no. 2 (1963), pp. 1-80; Felix Paukert, "Income Distribution at Different Levels of Develop- ment: A Survey of Evidence," International Labour Review, vol. 108, nos. 2-3 (August and September 1973), pp. 97-124; Irma Adelman and Cynthia Taft Morris, Economic Growth and Social Equity in Developing Countries (Stanford, Calif.: Stanford University Press, 1973). FRAMEWORK OF ANALYSIS S their transition effort. But that distribution has substantially improved during two decades of rapid growth. This "deviant" record should therefore be of interest to academicians and policymakers. Although no two countries ever are alike, and deviant performance may be based on special circumstances, an examination of the relations between growth and equity in a country exhibiting such a deviant performance can help to isolate the critical elements of that performance. Only then is it possible to judge whether the underlying conditions, which seem to have had the effect of virtually eliminating the usual conflict between these two principal societal objectives in Taiwan, are sufficient elsewhere to permit somewhat greater optimism. Such optimism would not be based on the conclusion that achieving growth with equity is easy. Instead it would be based on the conclusion that some of the obstacles are made by man, not nature, and can thus be removed by changes in policy.

Framework of Analysis

The problem of growth with equity can, we believe, be fruitfully analyzed in the historical context. During the third quarter of this century, the less developed world experienced unprecedented growth, a phenomenon accompanied by a resurgence of interest in the theory of economic development. We therefore felt that a natural way to proceed was to construct a framework of analysis that takes advantage of this new stock of knowledge. In this respect, three dimensions common to many contemporary growth models are points of departure for the work of this volume: historical perspective, subphases of growth, and typological sensitivity. By historical perspective we mean that the quarter century after the Second World War can be viewed in most LDCS as a period of transition between a long epoch of agrarianism and an epoch of modern growth.8 There in fact are two periods in the history of

3. Latin American countries, for example, started the transition earlier than most LDCs. For general works on the subject see Simon Kuznets, Modern Eco- nomic Growth (New Haven: Yale University Press, 1966); John C. H. Fei and Douglas S. Paauw, The Transition in Open Dualistic Economies: Theory and Southeast Asian Experience (New Haven: Yale University Press, 1973); and John C. H. Fei and Gustav Ranis, "Economic Development in Historical Per- spective," American Economic Review, vol. 59, no. 2 (May 1969), pp. 386-400. 4 INTRODUCTION economic doctrine when economists have been interested in growth and income distribution. The first period is the age of the classical economists-Smith, Malthus, and Ricardo; it dealt with transition growth in western Europe. The second period is that after the Second World War; it deals with transition growth in the contemporary developing world. This setting of transition growth gives the problem of "growth with equity" its distinctive character. Moreover the economic content of transition growth includes recognition of the dualistic structure of most less developed countries: agricultural and nonagricultural production sectors coexist; the center of gravity gradually shifts from one to the other. The basic phenomena include modernizing agriculture, generating an agricultural surplus, accumulating real capital to provide nonagricultural employment, and reallocating labor from agricultural to nonagricultural pursuits. It is convenient and substantively important to divide the overall phase of transition growth into subphases. These subphases are related to marked changes in the system's endowment of resources and in the prevailing package of policies-changes which affect relative factor prices and shares, as well as the behavior and performance of the economy. Because the reallocated labor and the accumulated assets are largely owned by individual families, the phenomenon of transition growth clearly has important implications for the distribution of income among families. To take full advantage of this base of growth theory, an additional dimension particularly relevant to the analysis of FID must be added: the spatial perspective. By spatial perspective we mean that a distinction must be made in the typical LDc between urban families and rural families, depending on their location and occupational pursuits. Urban families live in and near the major population centers and overwhelmingly engage in nonagricultural production. Rural families are spatially dispersed and derive their income from agricultural and nonagricultural production, the relative proportions of which depend upon the locational pattern of industries and services. Thus the separation of rural and urban householdsis a basic analytical device used in this volume. We also find it useful to distinguish among various types of factor income accruing to families. Wage income and property income are examples. This separation is essential for our analysis both at the aggregate and the disaggregate levels. At the aggregate or holistic level, such a separation makes it possible to trace the inequality of family income to its various factor components and, in this way, FRAMEWORK OF ANALYSIS 5 to link that inequality to the theory of development for a dualistic economy. At the disaggregate level, an intensive search into the causes of inequality of particular factor components forms a complementary part of the inquiry. We must naturally be somewhat selective in choosing the focus for such disaggregate analysis. A case will be made that the causation of the inequality of family wage income can be singled out for more intensive study. The system's labor force usually represents the most important type of capital distributed among families: human capital. Moreover, in the course of development, a functionally specialized modern labor force will gradually be formed out of the more homogeneous unskilled labor force of the agrarian epoch. A differentiated wage structure obtains for this increasingly heterogeneous labor force, which is differentiated by such characteristics as skill, sex, education, and age. In addition, the rules of family formation-or the composition of families with respect to this stratified labor force-also undergo transformation, depending on the propensity of families and society to invest in education. It is evident that the inequality of family wage income, an important component of overall inequality, can in turn be traced to this pattern of family ownership of differentiated labor, as well as to the differentiated wage structure. A similar disaggregate study could have examined the ownership and accumulation of physical capital by families. The usual classification of assets suggests that capital assets also are highly heterogeneous. The portfolio choice of families appears, however, to be a much more complex problem that perhaps is less relevant to the study of family income inequality than its wage counterpart. In any case, we have not tackled it in this volume. The role of the public sector also changes in the transition to modern growth. First and foremost, LDC governments must set the policy environment for private economic activity through their actions with respect to foreign exchange, trade, domestic credit, tariffs, and so on. These actions-whether they work through the market by way of indirect controls or circumvent the market by way of direct controls-may be critical for the kind of growth path and the pattern of income distribution generated. Second, governments directly participate, at different times and to a greater or lesser extent, in productive activities through the ownership of public enterprises. Third, governments act through their tax and expenditure policies to affect FID after the fact, after the dust of production has settled. In this volume we attempt to tackle only one of these aspects: taxation. 6 INTRODUCTION

The organization of this volume should be viewed in the foregoing perspective. We first make an effort to acquaint the reader with the general story of transition growth and distribution in Taiwan, especially for the 1950s-a period for which precise FID data either do not exist or are deficient in quality and sectoral breakdown. Next, we focus on the period after 1964, when reasonably good and comprehensive data become available on income distribution. Our principal attempt is to forge a more precise link at the aggregate level between the family distribution of income and the theory of development in a labor surplus economy. We also attempt to dig more deeply into the causes of the equity or inequity of income distribution from a number of related disaggregate perspectives. The study of FID still is in a pretheoretical stage in which nmuchof the effort must be directed at examining the empirical evidence. By sorting out the essential from the nonessential and the relevant from the irrelevant, it is to be hoped that the relevant and the essential can then be integrated with the mainstream of economic ideas, especially those related to development theory. The problems of measurement and data, two crucial facets of empirical research, thus receive special attention in this introduction so that readers can maintain their bearings in the rest of the volume.

Problems of Measurement

How is inequality to be measured? The basic problem is the choice of an appropriate index of inequality [I(Y)] that can be computed when the pattern of income distribution [Y = (Y 1 , Y2, . . . , Y.) ] is given for n families. Many alternative indexes of inequality are in use, such as the Gini coefficient [GY], the Theil index, the Atkinson index, the Kuznets index, and the coefficient of variation. All of them are reasonable but arbitrary, because none has a conspicuous advantage over the rest. For reasons spelled out below, we have generally chosen in this volume to use the Gini coefficient. All measurements are ultimately motivated by certain theoretical considerations-or, more appropriately, theoretical intuitions-in the pretheoretical stage. In our attempt to link the distribution of family income to growth-the growth of human and physical assets over time-it is natural to distinguish several types of assets. An example is the familiar dichotomy between capital [K] and labor [L] in the mainstream of growth theory. Our basic choice of the additive PROBLEMS OF MEASUREMENT 7 dimension of income is based on the recognition that this is the only way to forge the necessary links to development theory. The pattern of family income [Y = ( Y1, Y2, . . ., Yn) ] is thus seen to comprise several additive factor components:

MODEL OF ADDITIVE FACTOR COMPONENTS

y = y + y2 + . .+ yr, where

Yi = (Yl, Yi, . . ., Yi). (i = 1, 2, . . , r)

Each factor income component [Fi] corresponds to a particular type of asset owned by the n families. The formulation of additive factor- components problems of this type is, with minor exceptions, a central and unifying theme of this volume. For example, in our attempt to link FID to growth theory, the two factor components are property income [EY] and wage income [Ey] for urban households (r = 2). Agricultural income [Y3] is added as a third component for rural households (r = 3).4 By letting W = (W1 , W2, . . ., W,) represent the wage income pattern and ir = (71, 7r2, ... , 7rn) the property income pattern, the pattern of family ownership of the labor force can be traced to certain demographic rules of family formation, and the pattern of family ownership of physical assets can be traced to the rules of saving. For a more intensive treatment of the wage income component, the labor force can be stratified by age, sex, education, and other characteristics. In the model of additive factor components, Y stands for the pattern of total family wage income; Fi for the wage income earned by a particular type of labor force, such as adult college- educated females. The observed structure of wages in part reflects labor attributes and in part such noncompetitive elements as nepotism and sex discrimination. Abstractly the problem can again be treated as a problem of additive factor components.5 In addition to the differences in human capital dictated by market forces, other differences are the result of labor market imperfections caused by government intervention, oligopoly power, and so on. For one such

4. This formulation is used to forge a link to the dualistic growth model in chapter three, Growth and the Family Distribution of Income by Factor Com- ponents. 5. This formulation is used in chapter four, The Inequality of Family Wage Income. 8 INTRODUCTION

intervention, taxation, the total family income before tax [Y] can be viewed as the sum of family income after tax [EY] and tax payments [y2]. Family income after tax can in turn be seen to comprise various categories of expenditure and savings; tax payments to comprise direct and indirect taxes.6 Abstractly the problem once again becomes one of additive factor components. When the pattern of total income is abstractly formulated as comprising additive factor components, a natural way to explain the 2 Gini coefficient of Y[G,] is to trace it to G(Y'), G(Y ), . ., G(yr). the factor Gini coefficients computed for the r factor components. If:

i=( Yl + Yi + ... + Yni)/ ( YI + Y2 + .. + Y.),2 (i = 1,2 . .,r)

the values of i [(UP1, P2, .. .,. XP)] correspond to the r factor income shares. It then is tempting to design a decomposition formula of the following type:

1 G, = 'P1G(Y ) + '2G( Y2) + ... ± 'rG(Yr), which states that total family income inequality [Ga] is the weighted average of the factor Ginis [G(Yi)]. It turns out that this is an approximation relevant only under special conditions. A major theoretical task of this volume is to design exact and approximate decomposition formulas of this type.7 The Gini coefficient is thus used in this volume not because of its greater familiarity or superior characteristics, but because it has the intrinsic additive property that makes it convenient for the design of decomposition formulas. The model of additive factor components differentiates among various types or sources of income and represents only one kind of framework for FID analysis. It happens to be the one we find useful for most of the purposes of this volume. There also are other general models, such as those which try to differentiate among various types

6. This formulation is used in chapter six, Taxation and the Inequality of Income and Expenditure. 7. Problems of this type are inherently technical and have therefore been consolidated in the five chapters constituting part two, The Methodology of Gini Coefficient Analysis. When the results of that discourse on methodology are discussed in part one, however, numerical examples and other pedagogical devices are used to enable the less technically inclined reader to follow the argument. PROBLEMS OF MEASUREMENT 9 of income recipient or income-receiving family. For such a model the pattern of total family income [Y] is abstractly segmented as follows:

Y = (Yb, Y2, ... , Yn) = (S1, S2, ... , S,), where

SI (Yr, Y2, ... , Yr,), SI = (Yri+i, Yl+ 2, .. ., Yr,),.

Each subvector ES, (i = 1, 2, . . ., r) ] represents a particular class of income recipients. For example, when r is 2, S1 and S2 can represent males and females or, what would be more pertinent to our work, agricultural households and nonagricultural households. This classification suggests that all families within each Si can be referred to as a homogeneous group. Consequently the abstract framework can be referred to as a homogeneous group model-or, mathematically, as a segmentation model. Abstractly an index of inequality can then be defined on all income recipients [I(Y)], as well as on each homogeneous group [I(Si) (i = 1, 2, . . . , r)]. I(Si) is to be called intragroup inequality. If Yi (i = 1, 2, . . . , r) is the mean value of the ith group, the income pattern obtained by replacing every Yi by its group mean becomes:

tR = UPY, fI, .. , 0), (]YI,YI, ... , I2 ,~0.... I

(Y1, YI2, . . ., Yr)]. While suppressing the intragroup inequality, this equation clearly brings out the intergroup inequality. Consequently I(R) is called intergroup inequality. In the homogeneous group approach, the purpose of any decomposition formula is to trace I(Y) to the intergroup effect I(R) and the intragroup effect I(S).8 Intrinsically the study of family income distribution is a technically complicated matter, precisely because of the concern with patterns of income over families, patterns that are represented by vectors. Because this volume is principally aimed at the general reader, the foregoing explanation has been to help identify the contours of part one, where the methods of analysis are summarized and the empirical

8. This model of homogeneous groups is used only in chapter five, Income Distribution and Economic Structure. The decomposition of I (Y) into intergroup and intragroup effects in essence is the analytical technique used in that chapter, where it also turns out to be more convenient to use the variance as a measure of inequality, not the Gini coefficient. 10 INTRODUCTION findings for Taiwan are presented. As noted earlier, the more technical aspects of decomposition are presented in part two. It is recommended that general readers turn to this part only after absorbing the essential ideas in part one.

Problems of Data

In this pretheoretical stage of inquiry, much of the effort must necessarily be inductive. Consequently the availability and quality of data become unusually critical issues. The foregoing discussion of the problem of measurement has already suggested the kind of data needed for the work of this volume. The model of additive factor components requires, for example, data on the total family income pattern [Y] and on the patterns of income components [FY] for all families involved. All such data must ultimately be based on household surveys. For Taiwan in the 1950s, only two surveys gathered data on the overall distribution of income: one was conducted in 1953; the other in 1959-60.9 In addition, surveys by the Joint Commission on Rural Reconstruction (JCRR) for 1952, 1957, 1962, and 1967 contain information only on farm family incomes.'" Both sets deal with the total income of these families, not with factor income components; neither set is of good quality. In 1964, however, the Directorate- General of Budget, Accounting, and Statistics (DGBAS) began to conduct household surveys which included information on factor components, as well as total family incomes." In 1966 the DGBAS

9. Kowie Chang, "An Estimate of Taiwan Personal Income Distribution in 1953-Pareto's Formula Discussed and Applied," Journal of Social Science, vol. 7 (August 1956); National Taiwan University, College of Law, "Report on Pilot Study of Personal Income and Consumption in Taiwan" (prepared under the sponsorship of a working group of National Income Statistics, Directorate- General of Budget, Accounting, and Statistics (DGBAS); processed in Chinese). 10. See Y. C. Tsui and S. C. Hsieh, "Farm Income in Taiwan in 1952," Eco- nomic Digest Series, no. 4 (Taipei: Joint Council on Rural Reconstruction (JcRR), 1954) and JCRR, Rural Economics Division, "Taiwan Farm Income Survey of 1967-with a Brief Comparison with 1952, 1957, and 1962," Economic Digest Series, no. 20 (Taipei: JCRR, 1970). 11. DGBAS, Report on the Survey of Family Income and Expenditure, Taiwan Province, Republic of China, 1964 and subsequent years (Taipei: DGBAS). PROBLEMS OF DATA 11 broadened the classification to distinguish between rural and urban households. These data represent the principal data source for the formal analysis of this volume. The decomposition analysis could thus be carried out only for the years beginning with 1964; the separation of urban and rural households, for the years beginning with 1966.12 Even when good household surveys became available after 1964, specific dimensions of the data needed to be recognized and addressed. There are problems associated with the randomness of sampling and the biased nonresponses among sample returns. There are problems associated with differences between primary and published data- problems which cause the appearance of a "consolidation error." There are problems associated with data interpretation, especially in relation to the imputation of the functional shares and the spatial characteristics of economic activities. Although these by no means exhaust all the data problems in this field of inquiry, they are the ones directly relevant to the theoretical focus of the analysis in this volume.'3

Data quality

For surveys the DGBAS began to conduct in 1964, a sharp distinction must be made between the published data and the primary data contained in the original questionnaires. Only the published data are available to the public; what is published obviously is severely constrained by what is viewed as the effective consumer demand for particular combinations of primary information. As it is, a typical DGBAS volume contains more than 700 pages of tables, but will nevertheless disappoint many prospective data users. To illustrate this point, suppose that workers are classified by sex (male and female), education (primary, junior high, senior high, professional

12. The city of Taipei originally was part of Taiwan Province and was included in the overall DGBAS surveys.Since 1968Taipei has been reclassifiedas a special municipality; the Taipei City government, not DOBAS which is a provincial organization,has accordinglycarried out the same householdsurveys. For comparabilitywe have merged the two sets of data by adding, for each in- comebracket, both the familiesand incomesof thoseliving in the city of Taipei. 13. For example,the issuesof life-cycleincome and family lineageare among the dimensionsof FID analysis not addressed. To have formally treated these issueswould have raised even more severe problemsof data constraints. 12 INTRODUCTION school, and college), and age (subdivided into nine age groups). These three characteristics alone imply the existence of 90 kinds of labor-180 if rural and urban households are distinguished. Such an exhaustive cross-listing can be conveniently preserved only in coded tapes, not in published data.' 4 There is no question in our minds that the DGBAS surveys were based on competently drawn and stratified random samples. Even when samples are random, however, a frequent problem is the underresponse of certain groups, such as wealthier families. The conscientiousness of DGBAS personnel and the good attitude of respondents to questionnaire surveys nevertheless give us a high degree of confidence."' In addition, we know of no reason to suspect differences in the quality of the data over time. We are, moreover, mainly concerned with interpreting the changes rather than the precise levels of, say, the Gini coefficients. It should also be noted that even if the information reported by the households is perfect, the data may not give the functional income distribution as the economist would like to have it. In urban family enterprises, for example, it is difficult to differentiate between the entrepreneurial income of an owner-operator and his income as a skilled laborer. The problem is even more serious in a family farm, where there is less functional specialization. For the urban sector, DGBAS made its best effort to "impute" family income to the proper functional share, leaving only a small unallocated "mixed income" category. For the agricultural income of the rural families, no such imputation was made by the DGBAS or us. Consequently agricultural income is a mixed category that includes all property and wage income. For the spatial dimension, which also is important in the study of FID, the DGBAS data give the breakdown by "farm" and "nonfarm" households. We have taken these respective categories to

14. Published DGBAs data are used in chapters two, three, and five; coded DGBAs data in chapters four and six. Because a complete description of the data available to us should also focus on the design of questionnaires, the years of availability, and the absolute and relative sizes of sampies, we discuss these matters in an appendix to chapter four, where the original coded data are used for the first time. The use of published DGaAs data is discussedas it is deployed. 15. For analysis of this issue see Shirley W. Y. Kuo, "Income Distribution by Sizein Taiwan Area-Changes and Causes," in Income Distribution, Employ- ment, and Economic Development in Southeast and East Asia, 2 vols. (Tokyo: Japan EconomicResearch Center, 1975), vol. 1, pp. 80-146. PROBLEMS OF DATA 13 be proxies for "spatially dispersed rural households" and "spatially concentrated urban households."1 6 The quality of data must be judged in the context of the problems indicated. The inferences we derive from the data must be open to the criticism that conclusions should not be sensitive to small variations. On the whole, we feel that the quality of data in Taiwan favorably compares with that in other LDCS; we are quite confident that our findings are robust in this sense. We nevertheless recognize that the quality of data of this kind is such that stronger statements are not admissible. We therefore refrained from applying refined econometric tests in any of our applications.

Data aggregation Another problem is the consolidation issue associated with published data. Suppose there are n = 5,000 families. The published tabulation of the pattern of total family income [(Yi, Y2, . . ., Y,)] must then be in the form of decile or other income groups. By using such a tabulation, FID analysis tends to underestimate the degree of income inequality, because some intragroup inequality is inevitably suppressed. In the published DGBAS data, the number of income classes varies between 23 and 32; that represents a high degree of consolidation of sample survey returns for 3,000 to 6,000 families. Moreover the demand for international comparability required a somewhat higher degree of consolidation.1 7 Because of this consolidation, trends in the Gini coefficients over time once again become more meaning- fuil than the absolute magnitudes.

16. One survey year, 1968, contains in addition to the farm and nonfarm breakdown a locational breakdown into urban, semiurban, and rural residence. Because we are basically interested in the broad locational distinctions of urban residence in relation to rural residence, semiurban workers can thus belong to either the urban type of household or the rural. For 1968 the breakdown shows that about 80 percent of nonfarm households and more than 95 percent of farm householdsdirectly correspond to our urban (nonfarm) and rural (farm) sectors (households). In the absence of ideal data, we thus have confidence that the results of our empirical research give a relatively accurate picture of the effect of growth on FID in a dualistic economy. 17. In chapter three we tried to preserve the possibility for international comparisons by reprocessing our data to conform to the decile grouping convention of the World Bank. See for example Shail Jain, Size Distribution of Income (Washington, D.C.: World Bank, 1975). 14 INTRODUCTION

Using grouped data for the analysis of additive factor components is a new and important problem. It is new in its application to the particular methodology used by us and thus is not dealt with in the existing literature.'8 It is important because everyone is using grouped data and the international comparisons based on those data. We admit that this volume raises these and associated problems without being able to resolve them. They are shared by virtually all researchers now investigating income distribution, and this gives us some comfort. The fact that we lean heavily on the interpretation of changes in Ginis over time, not on the interpretation of the absolute levels of Ginis at different times, gives us additional comfort. Consequently our quantitative conclusions, like those of others, must be read with these qualifications in mind. We should add, moreover, that these problems are being tackled on at least two fronts. On the theoretical front, considerable progress is being made by Graham Pyatt at the World Bank, Fei and Ranis at Yale, and Chow and Chen at the Academia Sinica in Taiwan. On the statistical front, ungrouped or computerized data are now becoming available in Taiwan-data which will enable us to implement the theory and determine just how much difference the extent of aggregation makes to the results. We believe this to be an exciting new area of future research, but one that will take considerable time to sort out.'9

Data interpretation The effort to tackle the relations between equity and growth, the main objective of this volume, involves matters of theory and the use of data to implement the theory. For the theory we have, in the main, chosen to introduce a method of decomposition by additive factor components. For the data we have used the Gini coefficient to describe the level and changes in the pattern of equity. In any such formulation, there always is the problem of interpreting "significant" or "insignificant" changes in magnitudes. Neither the theoretical formulations nor the data provide a firm basis for such judgments.

18. See for example Joseph L. Gastwirth, "The Estimation of the Lorenz Curve and Gini Index," Review of Economics and Statistics, vol. 54, no. 3 (Au- gust 1972), pp. 306-16. 19. The outline of these issues is fully presented in chapter twelve. PROBLEMS OF DATA 15

These judgments can be arrived at only in reference to some con- sensual convention or standard derived over many years of research and observation. Such a consensus exists, say, for per capita income and population growth; it does not yet exist for measures of the equity of income distribution. The experience with international and inter- temporal comparisons on national income and population growth does permit judgments about the significance or insignificance of changes to be made with some confidence. In the realm of the Gini, however, we do not yet have a similar experience. Our description of change thus reflects more of our own judgments, which cannot as yet be checked against an agreed-upon convention.2T As more empirical work, especially in international comparisons, accumulates in this relatively new field, we will be in a better position to make qualitative statements. Meanwhile the reader is asked to take our own judgments about the significance of quantitative results with a grain of salt.

20. We especially wish to thank Tony Atkinson for bringing this point home to us.

PART ONE

The Case of Taiwan

IN CONTEMPORARY LDCS the issue of growth with equity must be viewed in the historical context of attempts by these countries to make the transition from their agrarian heritage to the epoch of modern growth. In analyzing equity during this transition, a framework is developed to link the distribution of family income to the store of growth theory which has been accumulating over the last quarter of a century. Central to this framework is a decomposition technique which makes it possible to trace the inequality of family income to various components of factor income and to various groups of income recipients. This approach, we believe, reflects the needs of the current pretheoretical stage of analysis and permits the systematic processing of data accumulated in recent years. Chapters one and two outline the case of Taiwan in the context of transition growth in the open, dualistic, labor-surplus economy. The crucial phenomenon for focus is the relatedness between the reallocation of domestic labor from agricultural to nonagricultural activities and the pattern of foreign trade. Upon examination, postwar development seems to be marked off by well-defined subphases of transition growth: a subphase of primary import substitution in the 1950s and a subphase of primary export substitution in the 1960s.Toward the end of the 1960s,the condition of labor surplus seems to have become gradually exhausted, as marked by substantial increases in unskilled real wages. Analysis of the family distribution of income (FID) over the entire period of transition must be related to this background. Chapter two concentrates on an analysis of distribution during the subphase of import substitution, for which the inadequacy of data on income distribution does not permit a fully rigorous analysis. Sub-

17 18 THE CASE OF TAIWAN sequent chapters analyze the distribution of income during the 1964-72 period, for which the data are much better. In chapter three a dualistic model is used; it contains rural and urban sectors, each with a number of households. With such a model, the impact of growth on the equity of FID over time is measured by the Gini coefficient [Gj] and analyzed by a method of additive factor Gini decomposition. According to this method, the impact of growth on the equity of FID is traced, both quantitatively and qualitatively, to three causal factors: a reallocation effect, a functional distribution effect, and a factor Gini effect. Each effect is explained and related as closely as possible to the theory of development. The functional distribution effect captures changes in the functional distribution of income-that is, the relative shares accruing to capital and labor. The reallocation effect captures changes in the share of agriculture in total income and the extent to which the center of gravity in the dualistic economy has, or has not, shifted. The factor Gini effect captures the impact of changes in the inequality of factor income- that is, the inequality of wage income [G.], property income [G,], and agricultural income [G0] taken separately. Development theory within the context of the dualistic economy can adequately explain only the impact of the reallocation effect and the functional distribution effect on G, over time. To increase understanding of the factor Gini effect, which the empirical work of this volume indicates may be quantitatively important, a fuller inquiry into the causation of the inequality of particular important factor incomes is required. Chapter four accordingly concentrates on the causation of the inequality of family wage income, which is the largest component of family income. At least two nonconventional aspects of modernization or development enter into this analysis. First, the formation of a modern labor force leads to recognition of the growing importance of labor heterogeneity as workers are stratified by such attributes as age, sex, and educational attainment. Second, the rules of family formation regulate the composition of family ownership of various types and qualities of labor. In this effort at disaggregate analysis, the competitive and discriminatory elements in the wage structure are analyzed by means of a multiple correlation analysis. On the basis of this information, as well as that relating to family membership and formation, a first-cut determination of the basic causes of wage income inequality among families is attempted. The model of additive factor components is used in this chapter as well. Chapter five further analyzes the inequality of total family income, THE CASE OF TAIWAN 19 but disregards the functional additive components of family income and classifies the income-receiving families by various criteria. For example, (Yi, Y', Y3), (Yi2, Y", Y", Y4), (Yl, Y2, Y3) represents the classification of ten families into three homogeneous subgroups. Whenever such a classification or segmentation is attempted, the inequality of total family income can be traced to an intergroup inequality effect and an intragroup inequality effect. Substantively three explanatory classifications are used: farm and nonfarm families; the degree of urbanization of the families; and characteristics of the head of household, such as age, sex, and educational standard. This chapter thus attempts to throw additional light on the causes of income inequality by pointing to differences in family attributes as causation factors. Chapter six examines inequality in the disposition of family income. If Y = (Y1 , Y2, . . . , Y.) is the pattern of family incomes before tax, then the family income pattern after tax [V = (VI, V2, ... ,I V,)] will be different because of the payments of direct tax [(T T, ., T])] and indirect tax [(Ti, T2, . .. , T) ]. The degree of inequality of family income before tax EGa] and after tax [Gv] may also be different, depending upon the progressiveness of direct and indirect taxes. One issue with very obvious policy implications is the impact of taxation on the equality of FID after taxes. The pattern of family income after tax [V] is after all only a means to family economic welfare. That income will in turn be disposed of by the families in various ways, leading to various patterns of family consumption [C' = (Ct, C2, ... , C')9] and saving ES = (S, S2, Sn) ]. The inequality of family income after tax EG[]will thus lead to inequality of family savings and family expenditure on education and other consumption categories, depending on the ways in which incomes are disposed of. A second issue studied in this chapter is the relation of the inequality of expenditure [G (Ci)] and saving [EG] to the inequality of family income after tax [EG]. The inequality of family investment in physical and human capital may be regarded as the primary causes of the persistence of family income inequality over the longer run. Persistence of the inequality of family consumption in particular consumption categories, such as housing or other items of conspicuous consumption, indicates the existence of class distinctions and points to possible targets for additional consumption taxation calculated to reduce the social impact created by family income inequality. The model of additive factors components is again used in this chapter. 20 THE CASE OF TAIWAN

Chapter seven summarizes the principal analytical findings and presents the policy conclusions that can be derived from these findings. As stated earlier, a fully deterministic theory of the distribution of income-one that is behaviorally specified-frankly is still beyond reach. We nevertheless believe that we have pointed out some directions that future work might take at the aggregate and disaggregate levels. Meanwhile there is no possibility of a moratorium on policy for those wanting to ameliorate existing or potential conflicts between strategies for growth and equity. Thus, although our analysis is by no means complete or comprehensive, we feel it important at this stage to try to derive the main conclusions for policy. Part two is devoted to a systematic derivation of the various decomposition formulas and equations used in part one. There are two reasons for postponing the discussion of technical issues. First, by gathering most such matters into one part, it is easier for the interested reader to appreciate the relatedness of the various methods used in this volume, to each other and to other contributions in the literature. Second, the less technically inclined reader can absorb the main argument of the early chapters without the periodic intrusion of an undue amount of technical detail. CHAPTER 1

Historical Perspective

THE BROAD OUTLINES of Taiwan's social and economic development during the postwar period are relatively well known. Although there is no unanimity concerning the transferability of this experience to other nations, there is general agreement that Taiwan's success is rare among less developed countries (LDCS). Two of Taiwan's achieve- ments in the years after 1953 are particularly notable: extremely rapid rates of economic growth were accompanied by improvements in the family distribution of income; unemployment, or underemployment, was virtually eliminated by the end of the 1960s. This success may in part be attributed to the legacy of the Japanese colonial era. The Japanese left behind an excellent physical and human infrastructure upon which Taiwan could later build growth in agriculture and industry. Moreover the influx of high-level manpower from the mainland more than compensated for the with- drawal of Japanese human resources after the war. As a result of these and other factors facilitating reconstruction, all output indicators in 1953 were roughly back to their prewar levels. The difference was that the economy, poised for takeoff, was engaged in purposive national development.

The Colonial Legacy

Patterns of colonial investment and resource flows in Taiwan had features recognizable in most LDCS: the colony supplied the colonizing country with primary products, in this case sugar and rice; in return, the colonizing country supplied the colony with

21 22 HISTORICAL PERSPECTIVE manufactured consumer goods.' Until the Second World War altered Japanese priorities, there was little encouragement of domestic industry beyond the processing of agricultural goods for export and the construction and operation of utilities required to support this processing. Somewhat less typical, however, was that Japanese colonial activity in Taiwan focused on food production. This focus led to the maintenance and expansion of an extensive, well-distributed irrigation system and to the organization of an islandwide network of farmers' associations and cooperatives. The Japanese, in their occupation of Taiwan from 1895 to 1945, sought to develop the colony into an agricultural supplier for Japan. All government activities during this period were directed toward this goal. At the same time Taiwan received a substantial inflow of physical, human, and institutional capital from Japan, and economic growth was considerable. Between 1910 and 1945 the population increased by 58 percent, net domestic product by 178 percent, agricultural production by 133 percent, industrial production by 267 percent, and export volume by 361 percent. Agriculture, which dominated the economy, was in turn dominated by rice and sugar cane. During 1935-37 rice accounted for 53 percent of the total value of agricultural output; sugar cane for 15 percent. The Japa- nese strongly encouraged the production of both crops, which together constituted 72.7 percent of Taiwan's total exports during 1930-39. During 1906-40 the production of rice grew at an annual rate of 2.7 percent; the production of sugar cane, at 4.5 percent. To encourage agricultural production the Japanese undertook a variety of projects to develop the physical, human, and institutional infrastructure of rural areas. They built an efficient and inexpensive system of railroads and rural roads to facilitate the transport of rural production. They brought in massive quantities of fertilizer from Japan and introduced new farming techniques to increase the productivity of the land. They constructed an extensive irrigation system: between 1910 and 1942 the area of land under irrigation increased from 227,000 hectares to 545,000 hectares; the total area under cultivation increased from 519,000 hectares to 837,000 hectares. Even with that increase in the total area under cultivation,

1. Discussion of the colonial period is largely based on Samuel P. S. Ho, Eco- nomic Development in Taiwan: 1860-1970 (New Haven: Yale University Press, 1978). THE COLONIAL LEGACY 23

Table 1.1. Distribution of Land and Owner-Cultivator Households, by Size of Holding, 1920, 1932, and 1939

Average Distributionof Distribution size of owner-cultivatorhouseholds of land holding Size of (percent) (percent) (chia) holding (chia), 1920 1932 1939 1920 1920

0-0.5 42.7 38.4 43.2 5.7 0.24 0.5-1 21.4 20.9 20.9 8.7 0.72 1-2 17.5 18.7 17.2 13.9 1.42 2-3 7.1 8.1 7.4 9.7 2.45 3-5 5.7 6.7 5.6 12.3 3.81 5-10 3.7 4.5 3.7 14.1 15.50 Over 10 2.1 2.7 2.0 35.8 1.

Total (chia) 405 ,181b 340,674 431,366 721,252

- Not applicable. Source: Samuel P. S. Ho, Economic Development in Taiwan: 1860-1970 (New Haven: Yale University Press, 1978). a. One chia is equal to 0.97 hectare or 2.47 acres. b. Because of the poor quality of the survey for 1920, this figure is generally considered to be too high.

the index of multiple cropping rose from 115.1 for 1911-15 to 125.3 for 1941-45. The Japanese also set up farmers' associations to give farmers advice on modern agricultural practices and rural credit cooperatives to provide agricultural finance. Health and education received considerable attention as well: the average life span rose significantly during the colonial period; the literacy rate rose from 1 percent in 1905 to 27 percent in 1940. The distribution of farm families and farmland by size of holding did not change very much in the twenty years before the Second World War (table 1.1). Nor did the distribution of families and land by type of cultivator change very much (table 1.2). It may thus be inferred that the distribution of land in 1945, when Japanese rule came to an end, probably was not very different from that during 1920-39. The poorest 40 percent of households (with less than 0.5 chia) owned less than a tenth of the land; the wealthiest 2 percent (with more than 10 chia) owned more than a third of 24 HISTORICAL PERSPECTIVE

Table 1.2. Distribution of Farm Families and AgriculturalLand, by Type of Cultivator,1920-22, 1927-30, and 1939-40

Item and type of cultivator 1920-22 1927-80 19S9-40

Total farm families 385,277 411,377 429,939 Distribution of families (percent) Owner 30.3 29.1 32.0 Part-owner 28.9 30.7 31.2 Tenant 40.8 40.2 36.8 Distribution of land (percent) Owner 41.9 43.8 43.7 Tenant 58.2 56.2 56.3

Total agricultural land (hectares)a 670,567 762,289 827,886

Source: Ho, Economic Developmentin Taiwan. a. Total area surveyed. the land. The pattern of tenancy reveals further inequity: about 40 percent of households were landless tenant households; they worked almost 60 percent of the cultivated land. Industrial activity during the colonial period also deviated from the typical colonial pattern. First, rather than serving mainly to facilitate primary exports to Japan, industry in Taiwan focused heavily on industries which either used the output of the agricultural sector or provided inputs to that sector. A survey of industrial activity in 1930 indicates that food processing accounted for 64 percent of registered factories, 55 percent of factory employment, and 76 percent of gross value of factory production. Sugar was by far the most important commodity; its share in total factory production during the 1930s was about 50 percent. The chemical and ceramic industries accounted for about 10 percent of total production. Both industries used raw materials readily available in Taiwan and were linked to the agricultural sector, which used by-products of sugar processing. Most of Taiwan's colonial industry thus was a direct extension of agriculture. In 1940 Taiwan had 8,940 factories which employed 128,000 THE COLONIAL LEGACY 2 workers. The vast majority of factories employed fewer than five workers and were establishments processing food, primarily rice. The capitalization of firms reflects the same pattern of small-scale operations: in 1936 the six largest firms accounted for 80 percent of paid-up capital. There was, in addition, a sizable handicraft sector, which accounted for 25 percent of manufacturing employment. To meet the power demands of the infant industrial sector, the Japanese invested heavily in power generation. Between 1926 and 1941 the capacity for power generation increased by 700 percent to levels that were reached again only in 1954 after the reconstruction of wartime damage. The Japanese controlled most of this infant industrial sector in Taiwan, partly because of initially restrictive regulations regarding capital ownership and partly because of the lack of accumulated wealth by Taiwanese. In 1929 the Japanese owned three-fourths of all paid-up capital in industry. The larger joint-stock companies engaged in manufacturing accounted for 60 percent of total paid-up capital. The Japanese also owned sizable shares of commerce, mining, and unspecified limited partnerships. In contrast, Taiwanese capital was concentrated in traditional industries based on agriculture; these industries accounted for only 3 percent of total paid-up capital. Taiwanese ownership of businesses not based on agriculture was mainly in handicrafts, commerce, and traditional transport. Most of these businesses, such as rice mills and noodle factories, were small-scale operations. In all, the Taiwanese owned less than 10 percent of the joint stock in larger scale operations and 22 percent of the paid-up capital in industry. The objectives and actions of Japanese colonial rule in Taiwan were similar to those applied in most other colonies. The Japanese implanted a typical triangular mode of operation and segmented the domestic economy into two distinct sectors: a modern sector oriented toward exports, and a large, backward sector oriented toward traditional agriculture. For most colonies such segmentation led to the formation of two mutually exclusive enclaves having little or no interaction. But this pattern did not evolve in Taiwan for three reasons. First, the export commodities were agricultural in origin and were produced by the land-based peasant class. Second, modernization of the agricultural sector occurred without the introduction of the plantation system. Third, industrialization had its roots in agriculture, and the linkages between the industrial and 26 HISTORICAL PERSPECTIVE agricultural sectors were extensive and close. This high degree of integration and interaction between the economy's two domestic sectors greatly facilitated postcolonial development in Taiwan.

Primary Import Substitution, 1953-61

The beginning of a country's effort to make the transition from colonialism to modern growth is customarily assigned to the year of its political independence. Taiwan became independent of Japan in 1945 and mainland China in 1949, but 1953 is more appropriately regarded as the initial year of its transition. An economic system independent of the mainland economy did not begin to emerge until late 1949. The Taiwanese economy did not recover from the damage caused by allied bombing during the Second World War, or from the cutoff of such vital agricultural inputs as fertilizer, until about 1951. Nevertheless the influx of talented officials, managers, and entrepreneurs from the mainland minimized problems associated with replacing the Japanese colonial presence. By the time government promulgated the first four-year plan in 1953, Taiwan possessed an unusually good physical and institutional infrastructure, especially in agriculture. It also had a solid base of human resources to go along with the more common features of a surplus of labor on limited arable land. The first subphase of transition growth, common to virtually all developing countries, is primary, or first-stage, import substitution. It is characterized by the diversion of traditional export proceeds away from further expansion of the colonial enclave and toward investment intended to replace previously imported industrial consumer goods by domestically produced consumer goods. Primary import substitution proceeded at a rapid pace in Taiwan. It was aided by the customary package of diverse policies aimed at encouraging the emergence of a class of industrial entrepreneurs and by a good dosage of natural import substitution made necessary by the severe disruption of Taiwan's traditional trading channels. Whether defined in horizontal or vertical terms, this subphase came to an end in Taiwan by the late 1950s or early 1960s (figure 1.1). The policies Taiwan chose during the 1950s to effect the desired redirection of resources seem quite standard. Deficit financing by government and substantial rates of inflation accompanied the PRIMARY IMPORT SUBSTITUTION, 1953-61 27

Figure 1.1. Ratios of Imports of Nondurable Consumer Goods to Total Imports and Total Supply, 1953-72

Labor surplus Labor scarcity 20 Primary import Primary export econdary import and substitution substitution export substitution

10 -\\_

5 _ \\ _ _ - ,lIT¢//(M,+ D,)

O1 I I I I I I I I I I I I I I I I I I 19521954 1956 1958 1960 1962 1964 1966 1968 1970 1972 lff, = imports of nondurable consumer goods M = total imports Af, + D, = total supply Source: Kuo-shu Liang and Ching-ing Hou Liang, "Exports and Employment in Taiwan" (paper read at Conference on Population and Economic Development in Taiwan, December 29, 1975-January 3, 1976, Academia Sinica, Institute of Economics, Taipei; processed).

classic syndrome of overvalued exchange rates and import licensing. Close examination nevertheless reveals substantial differences from the classic syndrome, and these differences suggest that Taiwan's primary import substitution was mild in relation to that in other countries. Although agriculture was squeezed both directly and by way of international trade to help finance industrialization, it was not as relatively disadvantaged as is normal. The agricultural sector received favorable attention during the 1950s, primarily through major land reforms and the allocation of additional investment to rural infrastructure. Agriculture's terms of trade never dropped below 96 (1952 = 100) in the 1950s. This accomplishment is remarkable by any standard. Even interest rates, which normally are very low or negative in real terms during this subphase, were reasonably high after a reform in the mid-1950s. Interest rates, in addition to generating savings, thus performed an allocative function. Taiwan's overall economic growth was good during the 1950s 28 HISTORICAL PERSPECTIVE

Figure 1.2. Growth Rate of Real Gross National Product per Capita, 1953-72

Labor surplus Labor scarcity

10 Primary import Primary export 8 substitution substitution Secondaryimport ; 6 and export -substitution

2 -

I I l I I I I I I I I I I I Il I I I I 1952 1954 1956 1958 1960 1962 1964 1966 1968 1970 1972

Sources: Directorate-General of Budget, Accounting, and Statistics (DGBAS), National Income of the Republic of China (Taipei, 1975); Economic Planning Council, Taiwan Statistical Data Book (Taipei, 1975).

(figures 1.2 and 1.3). Despite formidable pressures of population growth, real per capita income rose at an average rate of almost 3 percent a year. As would be expected, the growth of nonagricultural output was rapid-8.7 percent a year. Although a high rate of increase of agricultural output would not be expected, that output in Taiwan grew at the average rate of 5.5 percent a year during this decade. Saving rates, fluctuating in the vicinity of 10 percent, were also respectable. In addition, the pattern of industrial growth, featuring technological choices that were compatible with Taiwan's comparative advantage and output mixes that were abnormally intensive in labor, led to annual rates of nonagricultural labor absorption of more than 3 percent. Foreign capital, mainly U.S. aid, also was important. It initially helped to stabilize the economy and subsequently enabled purchases of overhead capital and industrial producer goods beyond those procurable with Taiwan's earnings from primary exports alone. Much of Taiwan's initial success can be attributed to the relative mildness and flexibility of its regime of primary import substitution. This subphase inevitably runs out of steam as domestic markets PRIMARY IMPORT SUBSTITUTION, 1953-61 29

Figure 1.3. Ratios of Savings and Investment to Gross National Product, 1953-72

Labor surplu.s Labor scarcity

40 - Primary import Primary export Secondary import and substitution substitution export substitution 30-

' 20 -

10 _ SIG7NP

1952 1954 1956 1958 1960 1962 1964 1966 1968 1970 1972 I = investment S = savings

Source: DGBAS, National Income of the Republic of China (Taipei, 1975). for nondurable consumer goods are exhausted. Domestic markets in Taiwan reached that point of exhaustion by the late 1950s. Taiwan did not, however, move into secondary or backward-linkage types of import substitution, as is typical. Instead Taiwan shifted the strategy for industrial development from the domestic market to international markets. The economy's industrial entrepreneurs were of good quality to start with. By cutting their teeth in the domestic market, they matured sufficiently to compete abroad and to find new markets for their labor-intensive industrial consumer goods. The story of the policy reforms adopted in Taiwan to accommo- date export-led industrial expansion during the late 1950s and early 1960s is well documented. Chief among these reforms were the move toward a unified and realistic exchange rate, the relaxation of exchange controls, the reduction in the rate of effective protection, and the continuing modification of interest rates. Government promulgated nineteen major reforms in 1960 alone.2 Intended to increase production, liberalize trade, and establish a more realistic

2. For a detailed account see Neil H. Jacoby, U.S. Aid to Taiwan (New York: Frederick A. Praeger, 1966), pp. 85-103. 30 HISTORICAL PERSPECTIVE set of relative factor prices, these reforms helped to usher in a rad- ically different pattern of resource allocation during the second subphase of economic transition: primary export substitution.

Export Substitution, 1961-72

Several indicators reflect the change in direction of resource flows in Taiwan and the ensuing change in the structure of production. During the subphase of primary import substitution, the system continued to rely mainly on its land-based primary exports, supple- mented by foreign aid, to finance industrial growth. But the reversal was dramatic as industrial exports based on unskilled labor increasingly substituted traditional primary exports. By 1972 they accounted for more than 80 percent of total exports, compared with 10 percent in 1952 and 50 percent in 1962 (figure 1.4). Equally

Figure 1.4. Ratios of Exports of Primary Goodsand Industrial Goods to Total Exports, 1953-72

Labor surplus Labor scarcity

100i- Primary import Primary ezport Secondary import and substitution substitution export substitution

80 -

G 60 -

P- 40-

20 -

1952 1954 1956 1958 1960 1962 1964 1966 1968 1970 1972 Ei = exports of industrial goods E, = exports of primary goods E = total exports

Source: Economic Planning Council, Taiwan Statistical Data Book (Taipei, 1975). EXPORT SUBSTITUTION, 1961-72 31

Figure 1.5. Ratio of Exports to Gross National Product, 1953-72

Labor surplus Labor scarcity

40 Primary import Primary export Secondary substitution substitution import and 30 - export substitution 20- ~~ ~EIGNP 10 -

C I I I I I l I I l l I l I I I I I I I 1952 1954 1956 1958 1960 1962 1964 1966 1968 1970 1972

E = exports Sources: Same as for figure 1.2. dramatic was the increase in the trade orientation of this relatively small, open economy. With exports growing at rates of more than 30 percent by the end of the 1961-72 period, the export ratio advanced to nearly 40 percent (figure 1.5). Nor has it since slowed down: Taiwan's export ratio today is more than 50 percent, one of the highest in the world. Furthermore the industries that grew fastest during the 1960s were such light consumer goods as textiles and such intermediate goods as electronics. Both were internationally competitive because of the use of technologies extremely intensive in unskilled labor. Concurrently the productivity of agricultural labor-supported by earlier investments in rural infrastructure, an increasingly favorable policy environment, and new technologies and crops-increased at 6.6 percent a year during the 1960s, compared with 4.9 percent during the 1950s. These gains kept the prices of foodstuffs low, despite the pattern of rapid industrialization, and prevented a premature sharp rise in real wages. Because of all these developments, rates of absorption of nonagricultural labor doubled from 3 percent in the 1950s to more than 6 percent in the 1960s. Despite high, if declining, rates of population growth, the reserve of surplus labor in Taiwan was virtually exhausted by the end of the 1960s. As would be expected, the proportion of the labor force in agriculture continuously declined during the 1950s and 1960s. But even the absolute size of the agricultural S2 HISTORICAL PERSPECTIVE

Figure 1.6. Ratios of Agricultural and Nonagricultural Employment to Total Employment, 1953-72

Labor surplus Labor scarcity

8s Primary import Primary export Secondary import and substitution substitution export _substitution ~~~~~60~~ ~ ~ ~ ~ ~ n/

40- La,, 20 -

1952 1954 1956 1958 1960 1962 1964 1966 1968 1970 1972

Lna = nonagriculturalemployment L. = agricultural employment L = total employment

Source: Shirley W. Y. Kuo, "A Study of Factors Contributing to Labor Absorption in Taiwan, 1954-71" (paper read at Conference on Population and Economic Development in Taiwan, December 29, 1975-January 3, 1976, Academia Sinica, Institute of Economics, Taipei; processed).

work force began to decline after 1965 (figure 1.6). By about 1968 the rapid pace of labor reallocation had led to the end of labor surplus and the beginning of labor scarcity. The rapid rise in real wages of unskilled workers, most closely proxied by the wage series for female textile workers, indicates this transition (figures 1.7, 1.8, and 1.9). By returning to the aggregate indicators of performance, it can be seen that per capita growth rates, which were respectable during the subphase of primary import substitution, accelerated to new levels and reached almost 10 percent during the subphase of primary export substitution (see figure 1.2). This performance was achieved despite the virtual termination of concessional foreign assistance and its only partial replacement by private capital from abroad. Booming industrial exports, along with continuing and expanding agricultural surpluses, provided ample fuel for the economy's rapid progress. The domestic saving rate also indicates a regime of substantially more rapid growth during the 1960s (see figure 1.3). The EXPORT SUBSTITUTION, 1961-72 S3

Figure 1.7. Index Numbers of Real Wages of Males and Females in Manufacturing, 1953-72 (1964 100)

Labor surplus Labor scarcity

200- Primary import Primary export Secondary import and substitution substitution export substitution U 150 _

; 100 Females

50 _- le

1952 1954 1956 1958 1960 19621964 1966 1968 1970 1972

Sources: Taiwan Provincial Government, Department of Reconstruction, Report of Taiwan Labour Statistics, 1958, 1963, 1969, and 1973.

Figure 1.8. Index Numbers of Real Wages of Males and Females in Textiles, 1953-72 (1964 100)

Labor surplus Labor scarcity

200- Primary import Primary export Secondary import and ;, 15C substitution substitution export substitution

-~150-

,100 Females

50 5CMales

1952 1954 1956 1958 1960 1962 1964 1966 1968 1970 1972

Sources: Same as for figure 1.7. S4 HISTORICAL PERSPECTIVE

Figure 1.9. Index Numbers of Real Wages of Males and Femalesin Transportand Communications,1953-72 (1964 = 100)

Laborsurplus Laborscarcity

200 Primary import Primaryexport / substitution substitution

15 Males .. , , Secondaryimport and c 100 _ export substitution P-4 _--,,~~~Females 50 _ O I I I I I I I I I I I I I I I I I I I - ' 19521954 1956 1958 1960 1962 1964 1966 1968 1970 1972

Sources: Same as for figure 1.7.

rate virtually doubled between the 1950s and the 1960s and reached a prodigious 30 percent in 1972 to make Taiwan a net exporter of capital. Such effective functioning of financial, commodity, and labor markets during the 1960s was in part the result of the stabi- lization achieved with the help of policy reforms adopted early in that decade.3 The scarcity of unskilled labor after 1968 indicates that Taiwan's economic development was heading into a new subphase characterized by the need for higher levels of skills and greater capital intensity. But that subphase-which might be called secondary import and export substitution and which Taiwan had fully entered by 1973-is part of another story.' This volume is mainly concerned with a developing economy's pattern of income distribution as it

3. Note the contrast between a 9 percent average annual rise in the consumer price index (cPI) during the 1950s and a modest 2 percent average annual rise during the 1960s. 4. Because of the substantial cyclical noise in the data for 1973 and subsequent years, the statistical series and the analysis in this book generally have been terminated in 1972, the last year of the fifth four-year plan. Extreme inflation accompanied the economic boom of 1973; inflation persisted during the international recession of 1974 and most of 1975. EXPORT SUBSTITUTION, 1961-72 35

Figure 1.10. Gini Coefficients, 1953-72

Labor surplus Labar scarcity

¢ 0.60 Primary import Primary export Secondary import and substitution substitution export substitution n 0.50

E 0.40 -

0.30 -

1952 1954 1956 1958 1960 1962 1964 1966 1968 1970 1972

Source: Shirley W. Y. Kuo, "Income Distribution by Size in Taiwan Area- Changes and Causes," in Income Distribution, Employment, and Economic Developmentin Southeastand East Asia. 2 vols. (Tokyo: Japan Economic Research Center, 1975), vol. 1, pp. 80-146.

makes its way to the turning point when accelerated labor-intensive growth has mopped up underemployment. The pattern of income distribution in Taiwan for the 1953-72 period is summarized by Gini coefficients in figure 1.10.1 Although the observations for 1953 and 1959 are based on a small sample of low quality, the overall pattern indicates that the reduction of income inequality was substantial. Even if the two observations for the decade of import substitution are disregarded, the low levels of the Gini coefficient after 1964, when the data become much more reliable, and the generally downward trend between 1964 and 1972 are both striking. The distribution of income appears to have improved over the entire 1964-72 period, as it very clearly does after the advent of labor scarcity in about 1968. The pattern after 1968 would be consistent with the views of Lewis and the findings of Kuznets, Adelman, and Morris that equity can be expected to

5. The purpose here is to present a brief overview of trends in the distribution of income in Taiwan. Detailed analysis of this pattern, especially for the 1964-72 period, is a principal subject of this volume and is reserved for subsequent chapters, particularly chapter three. 36 HISTORICAL PERSPECTIVE improve along with growth once real wages rise in a sustained fash- ion after commercialization. The really interesting question raised by the relations between growth and equity in Taiwan is this: Why was the Gini coefficient virtually constant during the period of extremely rapid growth before commercialization began in 1968? The answer clearly could be of great interest to other LDCSbecause most of them still are a long way from conditions of labor scarcity. Two problems are of greatest policy relevance to them: whether the conflict between growth and equity can be eliminated, or at least mitigated, before basic conditions of labor surplus can be brought to an end; and how this conflict might best be eliminated or mitigated. It would be small comfort for policymakers in these countries to have to conclude that economic growth is compatible with an improved distribution of income only after real wages have begun to rise consistently for neoclassicalreasons. CHAPTER 2

EconomicGrowth and Income Distribution, 1953-64

DESPITE CONSIDERABLE WARTIME, DESTRUCTION, the physical and institutional infrastructure established under colonial rule in Taiwan was instrumental in the rapid growth of agriculture during the 1950s. The irrigation system, which extended over more than half of Taiwan's cultivated area, proved valuable in ensuring the equitable distribution of benefits of green-revolution technology. Linkages between agriculture and the rural-based food-processing industry led to a marked spatial dispersion of economic growth. This pattern later enabled the provision of substantial nonagricultural employment to farmers. Progress in public health and education during the colonial period provided the basis for a highly productive labor force in both agriculture and industry. In addition, the overwhelmingly Japanese ownership of manufacturing enterprises contributed to a more equal distribution of income in two ways: it reduced the concentration of industrial assets in private Taiwanese hands in the period immediately after independence; and it provided a source of industrial assets that could be distributed as compensation to landowners under the program of land reform. The preconditions for rapid economic growth and an improved distribution of income thus were considerably more favorable in Taiwan than in the typical developing country. This chapter probes the reasons for the apparent absence of a conflict between growth and equity in Taiwan, especially during the 1950s. Even if the level of the Gini coefficient, based on poor data for the 1950s, must be viewed with several grains of salt, it prob-

87 38 ECONOMIC GROWTH AND INCOME DISTRIBUTION, 1953-64

ably is true, contrary to the experience in most LDCS, that the family distribution of income (FID) substantially improved during the subphase of primary import substitution in Taiwan.' The following sections examine the distribution of assets and the conditions of production during this period, first in agriculture, then to a limited extent in nonagriculture. The chapter concludes with a discussion of inferences about the course of FID in the 1950s and early 1960s. In subsequent chapters the superior detailed data available after 1964 enable more rigorous analysis of the interplay of economic growth and FID duiing the subphase of export substitution, both before and after commercialization.

Land Reform

The land reform that government instituted between 1949 and 1953 probably was the most important factor in improving the distribution of income before the beginning of the subphase of export substitution in the early 1960s.2Although much of the reform took place before 1952, the year for which sample data on the distribution of income first exist, it continued to have its impact well into the 1950s. The reform thus remained an important factor in explaining improvements in FID during that decade. Land reform was initiated for several reasons. Although the Japanese had developed a substantial agricultural infrastructure in Taiwan, they paid relatively little attention to the distribution of land (see tables 1.1 and 1.2 in chapter one). Given the large class of tenants, competition for the scarce land was so fierce that the average lease was less than one year. As a result, rents often were equal to 50 percent of the anticipated harvest, especially in the

1. Kowie Chang, "An Estimate of Taiwan Personal Income Distribution in 1953-Pareto's Formula Discussed and Applied," Journal of Social Science, vol. 7 (August 1956); National Taiwan University, College of Law, "Report on Pilot Study of Personal Income and Consumption in Taiwan" (prepared under the sponsorshipof a working group of National Income Statistics, DGBAS; processed in Chinese). 2. Discussion of land reform draws heavily on Samuel P. S. Ho, Economic Development in Taiwan: 1860-1970 (New Haven: Yale University Press, 1978) and Chao-Chen Chen, "Land Reform and Agricultural Development in Taiwan" (paper read at Conference on Economic Development of Taiwan, June 19-28, 1967, Taipei; processed). LAND REFORM 39

more fertile regions. Contracts frequently were oral; rent payments had to be made in advance; no adjustments were made for crop failures. These conditions and practices left the typical tenant helpless in any dispute with his landlord. The record of landlord abuse and the need to meet the food demands of postwar Taiwan- which, in addition to its own increased population, included hundreds of thousands of mainland Chinese-laid the groundwork for reform.3 In addition, the principle of land ownership by the tiller, although never receiving much attention, had always been part of the ideology of the Chinese Nationalists. The loss of the mainland and the social unrest threatening in Taiwan made the redistribution of wealth a particularly important issue for government. Land reform was also considered to be an essential ingredient of agricultural growth and economic recovery. Moreover, it could be imposed by a government free of obligations and ties to the landowning class. Government's conception of land reform was broad. Strengthen- ing farmers' associations and other elements of organizational and financial infrastructure in rural areas was considered to be important. Moreover the repair of physical infrastructure, started as soon as Taiwan was retroceded to China and almost completed by 1952, increased the effect of land reform on both growth and equity. But the main component of the successful reorganization of the agricultural sector clearly was the three-pronged package of land reform: the program to reduce farm rents, the sale of public lands, and the land-to-the-tiller program. The first step taken to promote agricultural incentives and output was to reduce farm rents and thereby to increase the share of tenant farmers in crop yields. Promulgated in 1949, this program had five basic provisions: first, farm rents could be fixed at no more than 37.5 percent of the anticipated annual yield of the main crops; second, if crops failed because of natural forces, tenant farmers could apply to local farm-tenancy committees for a further reduction; third, tenant farmers no longer had to pay their rent in advance; fourth, written contracts and fixed leases of three to six years had to be registered; fifth, tenants had the first option to purchase land from its owners. The reform affected about 43 percent of the 660,000 farm families, 75 percent of the 410,000 part

3. In 1945 and 1946, 640,000 mainlanders moved to Taiwan. Kuang Lu, "Population and Employment," in Economic Developmentof Taiwan, ed. Kowie Chang (Taipei: Cheng Chung Books, 1968), p. 532. 40 ECONOMIC GROWTH AND INCOME DISTRIBUTION, 1953-64 owners and tenants, and 40 percent of the 650,000 hectares of private farmland. Prices of farmland immediately dropped: paddy field prices by 20 percent; dry field prices by more than 40 percent by December 1949 and a further 66 percent by 1952.4 Equally important, the requirement for written contracts and the fixing of standard reduced rents enabled tenants to benefit from their own increased efforts for the first time. This incentive was a primary ingredient of the sustained increase in Taiwan's agricultural productivity during the early 1950s. With higher yields and lower rents, the average income of tenant farmers rose by 81 percent between 1949 and 1952.5 These rising incomes enabled tenants to purchase land put up for sale by their landlords; about 6 percent of private farmland changed hands. Given the success of the program to reduce farm rents, government decided to accelerate the program initiated in 1948 to sell public land to tenant farmers. Formerly owned by the Japanese, about 170,000 hectares of public land, or about 25 percent of Tai- wan's arable land, were suitable for cultivation. Taiwan Sugar Corporation owned most of this land and leased part of it to tenant farmers. The program gave priority in land purchases to cultivators of public land and landless tenants. The size of parcels was limited according to predetermined fertility grades, and the average size was 1 chia. Selling prices were 2.5 times the value of the annual yield of the main crops; payments in kind were set to coincide with the harvest season over a ten-year period. In all, 35 percent of Tai- wan's arable public land was sold during 1948-53; 43 percent during 1953-58. With government setting the example of returning land to the tiller, the stage was set for the most dramatic component of the three-pronged package: the compulsory sale of land by larndlords. This program stipulated that privately owned land in excess of specified amounts per landowner had to be sold to government, which would resell that land to tenants. 6 The purchase price was set at 2.5 times the annual yield of the main crops. Landlords were paid 70 percent of the purchase price in land bonds denominated

4. Chen Cheng, Land Reform in Taiwan (Taipei: China Publishing, 1961), p. 310. 5. Cheng, Land Reform in Taiwan, p. 309. 6. Individual landowners were allowed to retain three chia of medium-grade land. Anthony Y. C. Koo, The Role of Land Reform in Economic Development- A Case Study of Taiwan (New York: Frederick A. Praeger, 1968), p. 38. LAND REFORM 41 in kind and 30 percent in industrial stock of four public enterprises previously owned by the Japanese. The selling prices and conditions of repayment were the same as those provided in the sale of public lands. This third program had a dual objective. The new owner- cultivators were encouraged to work harder because they would benefit from any increases in agricultural output. The landlords, deprived of the privilege of living comfortably off the land, were encouraged to participate in the industrial development of Taiwan through ownership of four large-scale industrial enterprises. Between May and December of 1953, tenant households acquired 244,000 hectares of farmland, or 16.4 percent of the total area cultivated in Taiwan during 1951--55.

Effects of land reform on the distribution of assets Tables 2.1, 2.2, and 2.3 summarize the extent of land reform and its importance for the redistribution of wealth in Taiwan. Because

Table 2.1. Area and HouseholdsAffected by Land Reform, by Type of Reform Type of reform Reduction Sale of Land-to- Total of farm public the-tiller redistri- Item rents land program bution, Area affected (thousands of chia) 256.9 71.7 193.6 215.2 Farm households affected (thousands) 302.3 139.7 194.9 334.3 Ratio of cultivated area affected to total areab (percent) 29.2 8.1 16.4 24.6 Ratio of farm households affected to total farm households (percent) 43.3 20.0 27.9 47.9 Note: Figures may not reconcilebecause of rounding. Source: Samuel P. S. Ho, Economic Developmentin Taiwan: 1860-1970 (New Haven: Yale University Press, 1978), p. 163. a. Comprises land distributed under the sale of public land and the land-to-the- tiller program. b. Total area is the total area cultivated in 1951-55. 42 ECONOMIC GROWTH AND INCOME DISTRIBUTION, 1953-64

Table 2.2. Distribution of Land and Owner-Cultivator Households, by Size of Holding, 1952 and 1960

Distribution of owner-cultivator Distribution Averagesize households of land of holding Size of (percent) (percent) (chia) holding (chia)a 1952 1960b 1952 19 6 0 b 1952 196 0b

0-0.5 47.3 20.7 9.9 5.2 0.23 0.30 0.5-1 23.3 45.9 15.1 30.5 0.72 0.81 1-2 16.9 15.3 21.1 19.3 1.39 4.58 2-3 5.7 14.8 12.3 30.3 2.42 2.50 3-5 3.9 2.7 13.2 10.2 3.79 4.58 Over 5 3.4 0.6 28.4 4.6 10.14 9.10

Total (chia) 611,193 776,002 681,154 948,738 - -

- Not applicable. Note: Table 1.1 in chapter one gives comparable figures for the prewar period. Source: Ho, Economic Developmentin Taiwan. a. One chia is equal to 0.97 hectare or 2.47 acres. b. Includes only individual farm households; excludes public and private commercial farms, which all are larger than 10 chia and account for about 6 percent of total land and less than 0.1 percent of the number of holdings. of the reform, the distribution of land holdings dramatically changed between 1952 and 1960. The rising share of families owning medium- sized plots of land ranging from 0.5 to 3 chia reflects this change: their share increased from 46 percent in 1952 to 76 percent in 1960. The largest rise was in the share of families owning between 0.5 and 1 chia. What is even more dramatic, the average size of holdings in all categories of less than 5 chia increased. The combined share in total land of families owning less than 3 chia increased from 58 percent in 1952 to 85 percent in 1960. The proportion of land cultivated by tenants fell from 44 percent in 1948 to 17 percent in 1959. The proport,ion of tenant farmers in farm families fell from 38 percent in 1950 to 15 percent in 1960. Although government compensated landlords for the land they were forced to give up, this compensation was only 2.5 times the standard annual yield; market values of land ranged between 5 and LAND REFORM 43

Table 2.3. Distribution of Farm Families and Agricultural Land, by Type of Cultivator, 1948-60

Item and type of cultivator 1948 1950 1953 1955-56 1959-60

Total farm families n.a. 638,062 n.a. 732,555 785,592

Distribution of families (percent) Owner n.a. 36.0 n.a. 59.0 64.0 Part-owner n.a. 26.0 n.a. 24.0 21.0 Tenant n.a. 38.0 n.a. 17.0 15.0

Distribution of land (percent) Owner 55.9 n.a. 82.9 84.9 85.6 Tenant 44.1 n.a. 17.1 15.1 14.4

n.a. Not available. Note: Table 1.2 in chapter one gives comparable figures for the prewar period. Sources: Family distribution from Ho, Economic Developmentin Taiwan; land distribution from Chen Cheng, Land Reform in Taiwan (Taipei: China Publishing, 1961).

8 times the annual yield. The exercisethus represented a substantial redistribution of wealth. The total value of wealth redistributed as a result of this price difference was equivalent to about 13 percent of Taiwan's gross domestic product (GDP) in 1952.7 Furthermore bonds used to reimburse landowners paid an interest rate of only 4 percent, substantially less than the prevailing market rates. Be- cause of the landlords' lack of experience in nonagricultural matters, most landlords did not place much value on the 30 percent of their compensation received as industrial stocks. They promptly sold the stocks at prices far below value. Most of their proceeds went to consumption; some went to investments in small businesses. The majority of landlords thus ended up being not much better off than the new owner-cultivators.8

7. Ho, Economic Development in Taiwan, p. 166. 8. T. Martin Yang, Socio-Economic Results of Land Reform in Taiwan (Hono- lulu: East-West Center, 1970). 44 ECONOMIC GROWTH AND INCOME DISTRIBUTION, 1953-64

Table 2.4. Distribution of Agricultural Income, by Factor, 1941-56 (percent)

Property

Year Land Capital Labor

Before land reform 1941 52.20 11.48 36.32 1942 51.99 11.44 36.57 1943 45.65 10.04 44.31

After land reform 1953 37.39 8.23 54.38 1954 38.05 8.37 53.58 1955 38.19 8.40 53.41 1956 36.28 7.98 55.74

Source: S. C. Hsieh and T. H. Lee, "Agricultural Development and Its Contri- butions to Economic Growth in Taiwan," Economic Digest Series, no. 17 (Taipei: JCRR, 1966).

Through the reduction of rents and the redistribution of assets, the land reform had a marked effect on the functional distribution of income. Between 1941 and 1956 the combined share of property in total agricultural income fell from 63.7 percent to 44.3 percent (table 2.4). The sharp reduction in the share of property income was thus accompanied by a broader distribution of that income. Two investigators estimated the shares of farm income by recipient before the land reform, using the 1936-40 average, and after the land reform, using the 1956-60 average.9 According to these estimates, the share of cultivators in farm income increased from 67 percent to 82 percent; the share of government and public institutions, which received repayments from new landowners, increased from 8 percent to 12 percent; but the share of landlords and money- lenders declined from 25 percent to 6 percent.

9. T. H. Lee and T. H. Shen, "Agriculture as a Base for Socio-Economic Development," in Agriculture's Place in the Strategy of Development, ed. T. H. Shen (Taipei: JCRR, 1974), p. 300. LAND REFORM 45

Reorganization of institutional infrastructure The institutional infrastructure of Taiwan's agriculture was extensively reorganized and improved during the 1950s. The farmers' associations and credit cooperatives, set up by the Japanese to facilitate agricultural extension programs and rice procurement, were top-down institutions dominated by landlords and nonfarmers. As a result, most farmers did not directly benefit from them. In 1952 government consolidated those institutions in multipurpose farmers' associations restricted to farmers and serving their interests. In addition to the original function of agricultural extension, the activities of farmers' associations expanded to include a credit department, which accepted deposits from farmers and made loans to them, and to provide facilities for purchasing, marketing, ware- housing, and processing.'0 The associations thus became clearing- houses for farmers, who controlled and maintained them and viewed them as their own creatures. The other major institutional reform affecting agriculture during the 1950s was the establishment of the Joint Commission on Rural Reconstruction (iCRR) by the U.S. Congress in 1948. Its main functions were to allocate U.S. aid, provide technical assistance, and help the Taiwanese government plan and coordinate programs for agricultural extension, research, and experimentation. Thus, while the farmers' associations provided the much-needed organizational structure at local levels and facilitated the efficient flow of agricultural surpluses to the industrial sector, the JCRR was a major catalyst. It funded and initiated many innovations in farming techniques, and it introduced new crops and new markets. For

10. Deposits of the credit divisions of farmers' associations increased from about NT$100 million to NT$2,700 million by the end of 1965. Loans increased commensurately. (At the time of writing, the new Taiwan dollar was equal to about US$0.025.) Wen-Fu Hsu, "The Role of Agricultural Organizations in Agricultural Development" (paper read at Conference on Economic Develop- ment of Taiwan, June 19-28, 1967, Taipei; processed). Also during this period, credit became available to farmers from the ScRR, government-owned banks, and government agencies and monopolies. Between 1949 and 1960 the proportion of farm loans provided through the organized money market rose from 17 percent to 57 percent. Ho, Economic Developmentin Taiwan, pp. 179-80. 46 ECONOMIC GROWTH AND INCOME DISTRIBUTION, 1953-64

example, the JCRR was behind the introduction of asparagus and mushroom cultivation, which led to the highly successful production and export performance of those commodities in the 1960s.

Agricultural Development during the 1950s

Land reform alone could not solve the primary constraint facing Taiwan's agriculture: the shortage of land for a rapidly growing agricultural population. Although an ever-increasing number of farmers left agriculture to live and work in Taiwan's expanding urban areas, the population pressure on farmland was severe, especially during the early 1950s. The agricultural population rose from 4.3 million in 1952 to 5.8 million in 1964, an increase of 33 percent. During the same period the total area of cultivated land remained nearly fixed, culminating in a decline of the average size of holding from 1.29 hectares per family to 1.06 hectares (table 2.5). Taiwan

Table 2.5. Parameters and Indexes of Agricultural Employment, Production, and Development, 1952-64

Item 1952 1956 1960 1964

Agricultural population (thousands) 4,257 4,699 5,373 5,649 Agricultural employment (thousands) 1,792 1,806 1,877 2,010 Cultivated land (thousands of hectares) 876 876 869 882 Cropped land (thousands of hectares) 1,506 1,537 1,595 1,658

Percentage of agricultural population in total population 52.4 50.0 49.8 46.1

Hectares of cultivated land Per farm family 1.29 1.17 1.11 1.06 Per capita on farm 0.21 0.19 0.16 0.16 Per agricultural employee 0.49 0.48 0.46 0.44 AGRICULTURAL DEVELOPMENT DURING THE 1950s 47

Table 2.5 (Continued)

Item 1952 1956 1960 1964

Indexes Agricultural population 100.0 110.4 126.2 132.7 Agricultural employment 100.0 100.1 104.7 112.2 Total agricultural production 100.0 121.0 142.8 178.7 Agricultural crop productiona 100.0 116.8 132.1 159.7 Output of crops and livestock 100.0 121.4 139.1 168.5 Agricultural crop production per worker 100.0 115.4 126.1 142.4 Man-days of labor 100.0 104.1 111.5 116.9 Agricultural crop production to man-days of labor 100.0 112.2 118.8 136.6 Man-days of labor to employment 100.0 104.0 106.5 104.2 Fixed capital 100.0 107.5 116.6 133.6 Working capital 100.0 151.5 169.7 240.2 Multiple cropping 171.9 175.5 183.6 188.0 Diversificationb 3.54 4.07 4.01 5.75

Sources: Parameters of land and population and indexes of production from Economic Planning Council, Taiwan Statistical Data Book, 1975, pp. 47-51; indexes of labor man-days, output of crops and livestock, working capital, and fixed capital from Ho, Economic Developmentin Taiwan, p. 245; index of diversification from Shirley W. Y. Kuo, "Effects of Land Reform, Agricultural Pricing Policy, and Economic Growth on Multiple Crop Diversification in Taiwan," in Economic Essays, vol. 4 (Taipei: National Taiwan University, Graduate Institute of Economics, November 1973); other indexes from calculations by the authors. a. Excludes forestry, fishing, and livestock. b. The diversification index is calculated for 181 different crops by the formula: 1/2 (value of each product/value of total products)2.

overcame these pressures in three ways: by the achievement of substantial increases in agricultural productivity at the intensive mar- gin; by the diversification of agricultural production into more profitable crops; and by the part-time reallocation of labor to nonagricultural activities, including off-farm employment for many members of agricultural families. The growth of the agricultural sector during the 1950s was impressive. The real net domestic product (NDP) by agricultural 48 ECONOMIC GROWTH AND INCOME DISTRIBUTION, 1953-64 origin increased by about 80 percent during the 1952-64 period, or at an average rate of 5 percent a year, even though agriculture's share in NDP declined, from 36 percent to 28 percent. Because the agricultural population increased by only a third, an agricultural surplus was assured. Although this 5 percent annual increase in net output during the subphase of import substitution is considerably smaller than that of the industrial sector, it still is an impressive figure by any international standard of comparison. It is even more impressive when two additional factors are considered: the natural fertility of the soil is low; the land frontier on the mountainous island already had essentially been reached. The growth in agricultural output could only be called dramatic. Between 1952 and 1964 total agricultural production, including forestry, fishing, and livestock, rose by 78 percent, with the production of crops alone rising by 59.7 percent (see table 2.5). These production increases were primarily the result of increased yields in traditional crops, but they were also the result of the introduction of new crops. While the yields of such traditional crops as rice increased 50 percent, the yields of relatively new specialty crops, such as cotton and fruits, increased more than 100 percent." Fixed capital in agriculture expanded by about 34 percent between 1952 and 1964 (see table 2.5). Much of this expansion was in irrigation and flood control facilities, which deteriorated during the war and were rebuilt and expanded during the 1950s. Farm buildings and other structures were added to and improved. The water buffalo was gradually replaced by small tillers and other small mechanical devices. Working capital increased even more dramatically than fixed capital, growing by 140 percent between 1952 and 1964 (see table 2.5). The continuous introduction of new seed varieties, re- sponsive to intensive fertilizer applications, and the gradual reduction in fertilizer prices and government restrictions enabled Tai- wan's total fertilizer use to grow by 91 percent over the same period.' 2 As livestock production grew by nearly 120 percent, more and more commercial feeds were imported. Further increases in working capital included widespread use of pesticides, a major postwar innovation which helped to reduce high losses caused by disease and insects.

11. Economic Planning Council, Taiwan Statistical Data Book, 1975 (Taipei, 1975), pp. 48, 53-55. 12. Taiwan Statistical Data Book, 1975, p. 58. AGRICULTURAL DEVELOPMENT DURING THE 1950s 49

Technology change, introduced mainly by such government- supported research agencies as the JCRR, clearly was a significant factor in generating the increased agricultural output.' 3 In 1960 Taiwan had 79 agricultural research workers for every 100,000 persons active in agriculture, compared with 60 in Japan, 4.7 in Thailand, 1.6 in the Philippines, and 1.2 in India."4 The research agencies successfully introduced new strains of rice and sugar and such new crops as asparagus and mushrooms, as well as pesticides, insecti- cides, and new agricultural tools and machinery. In the Hayami- Ruttan terminology, most of the technology change was of the chemical variety, not the mechanical.'" Taiwan's impressive success in agriculture can thus be attributed to many factors. Although the purpose of this volume is not to analyze these factors in detail, their relation to the distribution of income nevertheless is relevant to the argument here. Given the physical and organizational improvement of the environmental infrastructure and the pervasive package of land reform, farmers had the incentives and the tools to improve their situation during the subphase of primary import substitution, which usually dis- criminates against agriculture. Moreover the technology change seemed to be of a type that generally used labor and saved land and capital. Although the number of persons employed in agriculture increased by 12 percent between 1952 and 1964, the number of man-days increased by 17 percent (see table 2.5). Consequently the number of working days per worker steadily increased. In 1965 the average worker had 156 days of farm employment, compared with 90 days in 1946 and 134 days in 1952.'6 As a result, the number of working days per hectare of land increased from approximately 170 in 1948-50 to about 260 in 1963-65.17

13. Ho estimated that 44.9 percent of the growth of agricultural output during 1951-60 can be attributed to changes in total factor productivity, 10.3 percent to increases in crop area, and 34.7 percent to increases in working capital. Ho, Economic Development in Taiwan, pp. 147-85. 14. Ho, Economic Development in Taiwan, p. 178. 15. Yujiro Hayami and Vernon W. Ruttan, Agricultural Development in International Perspective (Baltimore: Johns Hopkins University Press, 1971), passim. 16. You-tsao Wang, "Agricultural Development," in Economic Development of Taiwan, ed. Kowie Chang, p. 176. 17. W. H. Lai, "Trend of Agricultural Employment in Post-war Taiwan" (paper read at Conference on Manpower in Taiwan, 1972, Taipei; processed). 50 ECONOMIC GROWTH AND INCOME DISTRIBUTION, 1953-64

Larger labor inputs to the cultivation of traditional crops and the diversification into new crops resulted in more intensive cultivation of land. Between 1952 and 1964 the multiple-cropping index increased from 171.9 to 188; the diversification index increased from 3.54 to 5.75 (see table 2.5). The shift toward such labor-intensive crops as vegetables and away from the complete dominance of the traditional crops of rice and sugar was continuous. As an indication of the labor intensity of vegetable cultivation, the cultivation of one hectare of asparagus requires 2,900 times the labor input of the cultivation of one hectare of rice. Despite the substantial increase in the absorption of labor in agriculture between 1952 and 1964, rural underemployment continued during the 1950sand has been estimated at about 40 percent.18 The smaller, poorer farms were especially unable to generate sufficient income or to keep the entire family fully employed. This pattern led to a small amount of net physical migration out of the agricultural sector, estimated at less than one percent annually during the 1950s. Mostly, however, farmers increasingly sought off-farm employment in the rapidly growing rural industrial sector. Consequently underemployment did not develop into as serious a problem as in most other LDCS.1 9 The pattern of agricultural growth and the participation in that growth by rich and poor farmers were the basic ingredients of the dramatic improvement in the distribution of income in Taiwan during the 1950s.

The Distribution of Assets and Industrial Growth

What can be said about the distribution of assets outside agriculture during this period? Obviously much less, but broad patterns nevertheless are indicative. The 56.6 percent share of the public sector in industrial output in 1952 characterized the Taiwanese economy in the early 1950s (table 2.6). This pattern was mainly

18. The estimation difficultieshere are well known, and the authors do not place much confidence in these numbers; 19. Ho, Economic Developmentin Taiwan, p. 158. Ho derived his figures from S. F. Liu, "Disguised Unemployment in Taiwan Agriculture" (Ph.D. disserta- tion, University of Illinois, 1966) and Paul K. C. Liu, "Economic Development and Population in Taiwan since 1895: An Overview," in Essays on the Population of Taiwan (Taipei: AcademiaSinica, Institute of Economics,1973). THE DISTRIBUTION OF ASSETS AND INDUSTRIAL GROWTH 51

Table 2.6. Distribution of Industrial Production, by Public and Private Otwnership, 1952-64 (percent)

Electricity, gas, Total Manufacturing Mining and water

Year Public Private Public Private Public Private Public

1952 56.6 43.4 56.2 43.8 28.3 71.7 100.0 1953 55.9 44.1 55.9 44.1 24.4 75.6 100.0 1954 52.7 47.3 49.7 50.3 32.5 67.5 100.0 1955 51.1 48.9 48.7 51.3 28.5 71.5 100.0 1956 51.0 49.0 48.3 51.7 26.5 73.5 100.0 1957 51.3 48.7 48.7 51.3 26.3 73.7 100.0 1958 50.0 50.0 47.2 52.8 24.2 75.8 100.0 1959 48.7 51.3 45.2 54.8 22.6 77.4 100.0 1960 47.9 52.1 43.8 56.2 24.2 75.8 100.0 1961 48.2 51.8 45.3 54.7 18.8 81.2 99.9 1962 46.2 53.8 42.3 57.7 19.6 80.4 98.6 1963 44.8 55.2 40.6 59.4 19.1 80.4 99.7 1964 43.7 56.3 38.9 61.1 20.5 79.5 98.8

Source: Economic Planning Council, Taiwan Statistical Data Book, 1975, p. 75.

a consequence of the Chinese takeover of Japanese assets at the end of the Second World War. In addition, before the evacuation from the mainland, the Nationalist government dismantled and shipped industrial equipment, such as textile spindles, and in some cases entire enterprises to Taiwan. Firms under public ownership were initially plagued with typical problems: inefficiency, over- staffing, rigid pay structures, and bureaucratic interference. Mean- while small firms and simple equipment characterized the private sector. As late as 1961, 31 percent of all manufacturing establishments employed fewer than ten workers.20 All industry was ham- pered by the shortage of foreign exchange.2 ' This situation undoubtedly was favorable to the equity of the

20. Ho, Economic Development in Taiwan, p. 597. 21. Council on U.S. Aid, Industry of Free China, vol. 1, no. 4 (1954). 52 ECONOMIC GROWTH AND INCOME DISTRIBUTION, 1953-64 initial distribution of industrial assets. Because private ownership of capital was not on a large scale, entrepreneurs generally were not in a position to gain monopolistic control of industries or to accumulate great wealth from property income. In the private sector the small size and labor intensity of firms was favorable to the share of workers. Profits of the larger, more capital-intensive firms went to government, not to private entrepreneurs. During the early 1950s government began transfering the four public enterprises under its control to private ownership: Taiwan Cement Corporation, Taiwan Pulp and Paper Corporation, Taiwan Industrial and Mining Corporation, and Taiwan Agriculture and Forestry Development Corporation. This transfer was not easily accomplished. Government had difficulty finding buyers because of the lack of accumulated private wealth and entrepreneurial exper- tise and because of the poor track records of these enterprises. In 1953 a large portion of government assets was nevertheless transferred as partial payment to landlords under the land-to-the-tiller program. As a result of this transfer and such other factors as the increasingly rapid growth of private industry, the government- owned share of total industrial production fell to 43.7 percent in 1964 (see table 2.6). Industries remaining in the public sector included utilities, railroads, shipbuilding, and iron and steel. Thus, despite the substantial drop in government ownership, the public control of assets continued to be important, particularly in the most capital-intensive industries, in which growth is least favorable to the distribution of income. Taiwan's industrial growth during 1952-64 was impressive: NDP grew at the average annual rate of 7 percent; the industrial sector at the average annual rate of 11 percent. By 1964 the real NDP of the industrial sector was more than 250 percent higher than in 1952; that sector's share in total NDP rose from 18 percent to 28 percent. Most of this growth was the result of the emergence of the manufacturing subsector: its share in NDP grew from only 11 percent in 1952 to more than 20 percent in 1964.22The concentration on food processing and textiles, as well as on other industries that typically predominate during the subphase of primary import substitution, continued to be heavy.

22. Taiwan Statistical Data Book, 1975, p. 28. THE DISTRIBUTION OF ASSETS AND INDUSTRIAL GROWTH 53

The reorientation of industrial output between the late 1950s and early 1960s is also reflected in the changing composition of imports and exports. Although total imports in constant prices more than doubled during the 1952-64 period, the share of imports of consumption goods in total imports rapidly declined from 20 percent to 6 percent. In constant prices those imports in 1964 were slightly below their 1952 level. Imports of raw materials for agriculture and industry kept pace with the growth of total imports. But imports of capital goods, such as machinery and electrical and transport equipment, almost quadrupled. This growth reflected the twin efforts to shift industrial activity away from the narrow domestic market toward wider international markets and to provide the physical infrastructure needed for that shift. Even though government policy was to reduce imports in the 1950s, total imports doubled during 1952-64. This expansion reflected the need to fuel import substitution during the 1950s, as is evidenced by the growth of imports of capital goods by about 20 percent a year before 1960.23Imports of raw materials, which were growing steadily at 8 percent a year during the 1950s, started to grow at 11 percent a year in response to the new opportunities of the export-substitution era. This policy of accelerated imports of raw materials, combined with the use of unskilled labor, was at the heart of the drive that followed for expanding labor-intensive industrial exports. As would be expected in any developing economy, imports continued to outstrip exports throughout the 1952-64 period in Taiwan. Exports in constant prices nevertheless quadrupled. Moreover, as noted earlier, industrial exports increased by a phenomenal 2,800 percent and dramatically changed the composition of exports. The share in total exports of agricultural and related exports declined from 92 percent to less than 60 percent in only twelve years; the share of industrial exports went up fivefold, from 8 percent to 40 percent. Industrial production and export growth during this period was concentrated in the textile, leather, and wood and paper industries. Most of the increase occurred between 1960 and 1964: that is, after changes in policies and factor endowment ushered in the subphase of export substitution.

23. See Carlos F. Diaz-Alejandro, "On the Import Intensity of Import Sub- stitution," Kyklos, vol. 18, no. 3 (1965). 54 ECONOMIC GROWTH AND INCOME DISTRIBUTION, 1953-64

Effects of Growth on Equity

Information about the family distribution of income (FID) in Taiwan is meager before 1964, when the Directorate-General of Budget, Accounting, and Statistics (DGBAS) began to conduct regular surveys. One investigator conducted sample surveys of overall income distribution for 1953 and 1959.24The JCRR conducted sample surveys of the income of farm families in 1952, 1957, 1962, and 1967.25 The Economic Planning Council conducted surveys of a very limited sample of urban wage and salary workers in 1955 and 1959.26

Rural FID Farm families have three types of income: the income from agricultural activities [Ya], a merged return to property (mainly land) and labor, is preponderant; it is augmented by wage income [Y-] and property income [YT] from rural industry and services. Table 2.7 gives the Gini coefficientsof total income and factor income and the distributive shares of factor incomecomponents for 1952, 1957,1962, and 1967.21In the followinganalysis, average farm-size groupingsare used as a proxy for average income-sizegroupings, which are not available.Because the data are groupedinto only a few intervals based on farm size, the resulting Gini coefficients undoubtedlyare lowerthan if there had been more intervals.Never-

24. Chang, "Estimate of Personal Income Distribution in 1953;" National Taiwan University, "Report on Pilot Study." 25. JCRR, "Taiwan Farm Income Survey of 1967-with a Brief Comparison with 1952,1957, and 1962," Economic Digest Series, no. 20 (Taipei: JCRR, 1970). 26. EconomicPlanning Council,"Family Income and Expenditure Survey of Wages and Salaries by Income Class, Taiwan Province" (Taipei, n.d.; processedin Chinese);idem, "Family Income and Expenditure Survey of City Con- sumers, Taiwan Province" (Taipei,n.d.; processedin Chinese). 27. The following notation will be adhered to throughout this volume in tables and text: the Gini coefficientof income from all sources is G,; the Gini coefficientsfor (merged) agricultural income, rural industry wage income, and rural industry property income respectivelyare G., G,, and G,; the distributive shares, or weights,of these kinds of incomeaccruing to farm familiesrespectively are O., O, and XT. EFFECTS OF GROWTH ON EQUITY 55

Table 2.7. Gini Decomposition Analysis Based on Farm Family Income Stratified by Size of Farm, 1952-67

Percentage changea

1952- 1957- 1962- Item 1952 1957 1962 1967 57 62 67

Gini coefficients Wage income [G.] n.a. 0.0631 0.0862 0.0823 n.a. 37 -6 Property income [Gr] n.a. 0.1662 0.0604 0.1116 n.a. -64 31 Agricultural income [G.] n.a. 0.3499 0.3641 0.3225 n.a. 4 -12 Total income [G,] 0.2860 0.2335 0.2126 0.1790 -18 -9 -14

Distributive shares Wage income [,0] 0.0580 0.2339 0.1969 0.2522 303 -16 24 Property income [01] 0.1630 0.1342 0.2124 0.1639 -18 58 -36 Agricultural income [0.] 0.7790 0.6320 0.5908 0.5840 -19 -7 -1

n.a. Not available. Sources: 1952 from Y. C. Tsui and S. C. Hsieh, "Farm Income in Taiwan in 1952," Economic Digest Series, no. 4 (Taipei: JCRR, 1954); 1957,1962, and 1967 from JCRR, "Taiwan Farm Income Survey of 1967-with a Brief Comparison with 1952, 1957,and 1962," Economic Digest Series, no. 20 (Taipei: JCRR, 1970). a. For 1952-67the changein G, was -37 percent, of which 1952-57accounted for -18 percent, 1957-62for -7 percent, and 1962-67for -12 percent; the changesin distributive shares were 335 percent for wageincome, 0.6 percent for property income, and -25 percent for agriculturalincome.

theless it still is possible to observe significant trends in movements of the Gini coefficient of total income after 1952 and the Gini coefficients of factor income after 1957.25 Throughout the 1952-67 period the Gini coefficient of total income [G,] declined by a remarkable 37 percent; it declined by 18

28. To the extent that the ranking of familyincome differs from, and is poorly proxied by, the ranking of familyfarm size,the Gini coefficientin table 2.7 tends to underestimate the true inequality of income. The authors have no way of checkingthe degree of this underestimation.The other issue addressedbasically is the error introduced when familiesare grouped by income ranges, a problem fully discussedin chapter twelve. 56 ECONOMIC GROWTH AND INCOME DISTRIBUTION, 1953-64

percent during 1952-57 alone, the heart of the subphase of import substitution. As import substitution ran out of steam because of the limitations of domestic markets, the pace of decline slowed down; the decline for 1957-62 was only 7 percent. Interestingly enough, the decline of the Gini coefficient picked up speed again after the policy reforms of 1960-61 got the new era of export substitution under way. The decline for 1962-67 was 12 percent. This figure is similar to the decline of 11 percent for 1964-68 obtained from superior DGBAS data. Hence, the trend of these results, if not the magnitude, would seem to be fairly reliable. The data for factor income components indicate that the distribution of agricultural income and wage income worsened between 1957 and 1962; that of property income improved. After export substitution got under way, however, the distribution of property income worsened; that of agricultural and wage income improved. What are the reasons for these patterns of the Gini coefficients of factor income over time? One reason is the increase in multiple cropping. The multiple- cropping index of farms smaller than 0.5 chia was about 25 percent higher than that for farms larger than 2 chia (table 2.8). This inverse relation between farm size and multiple cropping indicates that the poorer families cultivated their land more intensively,

Table 2.8. Multiple Cropping, by Size of Farm, 1952 and 1967 (single cropping = 100) Index of multiple cropping Size of farm (chia) 1952 1967

Less than 0.5 227 216 0.5-1 214 206 1-1.5 204a 197 1.5-2 204a 193 2-3 184b 190 More than 3 184b 161

Average 198 197

Sources: Same as for table 2.7. a. The 1952 average for farms of 1-2 chia applies to both categories. b. The 1952 average for farms larger than 2 chia applies to both categories. EFFECTS OF GROWTH ON EQUITY 57 either by introducing additional harvests in rice or adding high- valued, and usually more labor-intensive, secondary crops. The marked decline of the agricultural Gini [Ga] between 1962 and 1967 coincides with the introduction of mushrooms, asparagus, and other important secondary crops. This pattern implies that poorer farmers could take more advantage of this type of product-oriented technology change in agriculture. A second reason is that the high distributive share of agricultural income significantly declined, from 78 percent in 1952 to 58 percent in 1967; the share of nonagricultural income increased from 22 percent to 42 percent (see table 2.7). The increase in the share of wage income from 6 percent to about 25 percent is particularly noteworthy. These figures testify to a rapid reallocation of labor from agricultural to nonagricultural sources of income for the average farm family. The speed of this reallocation may be explained in a variety of ways. First, the phenomenon is closely associated with the pattern of industrial dispersion, which is an inmportant feature of industrialization in Taiwan. The rapid increase in the share of wage income may thus be traced to the rapid growth of rural industries, which provided employment to members of rural families. Second, associated with transition growth are certain institutional changes germane to commercialization and the functional specialization of tasks traditionally performed by members of farm households under family farming. For example, the replacement of the son as farm-to-market transporter by a transport firm, which hires the same son as a wage earner, reduces agricultural income and increases wage income. Much functional specialization of this type must have taken place during the transition, especially because of the spatial dispersion of nonagricultural production activities. But to adduce more about this important problem would require a different set of data and a more refined analytical design. A third reason for the movements in the Gini coefficients of factor income is the greater importance of off-farm wage income to poorer families than to wealthier families, at least when farm size is used as a proxy for income class (tables 2.9, 2.10, and 2.11). As the size of the farm increases, the share of nonagricultural income decreases. This pattern reflects the greater ability of poorer farmers to take advantage of nonagricultural income opportunities. For example, farm families holding less than 0.5 chia in 1957 earned a remarkable 61.9 percent of their income from nonagricultural activities; wage income accounted for 41.4 percent of their total income. In contrast, 68 ECONOMIC GROWTH AND INCOME DISTRIBUTION, 1953-64

Table 2.9. Average Income of Farm Families, by Size of Farm, 1952-67 (1952 N.T. dollars) Averageincome

0-0.5 0.5-1 1-2 2-4 Average Year and type of income chia chia chia chia size farm

1952 Total income 3,765 5,097 8,010 14,653 7,361 Wage income n.a. n.a. n.a. n.a. 427 Property income n.a. n.a. n.a. n.a. 1,200 Agricultural income n.a. n.a. n.a. n.a. 5,734

1957 Total income 5,015 6,873 9,481 16,606 8,613 Wage income 2,278 1,940 1,695 2,146 2,011 Property income 825 1,140 1,021 2,030 1,160 Agricultural income 1,912 3,793 6,765 12,430 5,443

1962 Total income 5,655 7,937 11,144 17,629 9,682 Wage income 2,355 1,890 1,565 1,775 1,906 Property income 1,835 1,883 2,229 2,462 2,056 Agricultural income 1,465 4,163 7,351 13,392 5,720

1967 Total income 9,920 10,754 15,302 24,962 13,727 Wage income 4,247 3,369 2,928 3,061 3,475 Property income 2,262 1,643 2,426 3,218 2,262 Agricultural income 3,411 5,742 9,946 18,684 7,990

n.a. Not avai:able. Note: At the time of writing, the new Taiwan dollar was equal to about US$0.025. Sources: Same as for table 2.7. the shares of nonagricultural income in total income were 44.8 percent for families holding 0.5 to 1 chia, 28.7 percent for families holding 1 to 2 chia, and 25.2 percent for families holding more than 2 chia. For these families the shares of wages in total income respectively were 28.2 percent, 17.9 percent, and 12.9 percent. Thus off- farm income, particularly wage income, clearly was an important EFFECTS OF GROWTH ON EQUITY 59

Table 2.10. Distribution of Factor Shares, by Size of Farm, 1952-67

Factorshare

0-0.5 0.5-1 1-2 2-4 Average Year and type of income chia chia chia chia size farm

1952 Wage income n.a. n.a. n.a. n.a. 0.0580 Property income n.a. n.a. n.a. n.a. 0.1630 Net agricultural income n.a. n.a. n.a. n.a. 0.7789

1957 Wage income 0.4142 0.2823 0.1788 0.1292 0.2338 Property income 0.2045 0.1658 0.1077 0.1223 0.1342 Net agricultural income 0.3813 0.5519 0.7135 0.7485 0.6320

1962 Wage income 0.4164 0.2381 0.1404 0.1007 0.1969 Property income 0.3245 0.2373 0.2000 0.1397 0.2123 Net agricultural income 0.2591 0.5246 0.6596 0.7597 0.5908

1967 Wage income 0.4281 0.3133 0.1913 0.1226 0.2522 Property income 0.2280 0.1528 0.1586 0.1289 0.1638 Net agricultural income 0.3438 0.5339 0.6501 0.7485 0.5840

Note: For each size category in each year, the sum of the shares of wage, property, and net agriculturalincome is 1.0000. Sources: Same as for table 2.7.

FID equalizer because it constituted a greater share of total income for the poorer farm families. Data on the extent of off-farm activity by farm families in 1960 give further support to this notion (table 2.12). Less than 50 percent of farm households engaged in full-time farming in 1960. What is more relevant, the percentage engaged in full-time farming generally increased with farm size. Among farm families with less than 0.5 hectares, only 30 percent engaged in full-time farming, and 35 60 ECONOMIC GROWTH AND INCOME DISTRIBUTION, 1953-64

Table 2.11. Distribution of Farm Households, Income, and Factor Shares, by Size of Farm, 1952-67

0-0.5 0.5-1 1-2 2-4 Item chia chia chia chia

1952 Total income 0.1535 0.1869 0.2367 0.4229 Households 0.3000 0.2700 0.2176 0.2124

1957 Total income 0.1752 0.2134 0.2936 0.3177 Wage income 0.3410 0.2581 0.2249 0.1759 Property income 0.2140 0.2629 0.2348 0.2884 Agricultural income 0.1057 0.1864 0.3316 0.3763 Households 0.3010 0.2675 0.2668 0.1648

1962 Total income 0.1596 0.2358 0.3352 0.2693 Wage income 0.3377 0.2853 0.2392 0.1378 Property income 0.2438 0.2634 0.3158 0.1770 Agricultural income 0.0700 0.2094 0.3743 0.3463 Households 0.2732 0.2876 0.2912 0.1479

1967 Total income 0.2193 0.2269 0.2943 0.2595 Wage income 0.3710 0.2808 0.2224 0.1257 Property income 0.3036 0.2104 0.2830 0.2030 Agricultural income 0.1296 0.2081 0.3286 0.3337 Households 0.3037 0.2896 0.2640 0.1427

Note: For each row the sum of the entries is 1.0000. Sources: Same as for table 2.7. percent had some kind of side income. In contrast, among farm families with more than 5 hectares, 61 percent were full-time farmers, and fewer than 10 percent had side incomes.2 9

29. The greater capacity of the richest farmers-that is, those with the largest holdings-to engage in nonagricultural rural activities as investors might explain why they again had somewhat higher nonagricultural participation rates; the greater necessity of the poorest farmers-that is, those with the smallest holdings-to take advantage of opportunities by offering their labor services probably explains their high participation. EFFECTS OF GROWTH ON EQIUITY 61

Table 2.12. Off-farm Activity of Farm Families, by Size of Farm, 1960 (percent) Farm Farming Farming Sideline workers Size of farm as only as main as main with (hectares) activity activity activity sidelines

Less than 0.5 30.1 26.7 43.2 34.8 0.5-1 55.6 35.4 9.0 17.9 1-2 65.2 31.7 3.1 11.9 2-3 67.3 30.8 1.9 9.3 3-5 66.5 31.5 2.0 8.5 More than 5 61.4 35.9 2.7 8.6

Total 49.3 30.9 19.8 20.0

Source: Ho, Economic Developmentin Taiwan, p. 157.

A 1963 study by the JCRR examined the character of such off-farm employment (table 2.13). This study found that 61 percent of men who found employment off their own farns were seasonal workers; of these, nearly 80 percent worked in farming, presumably at harvest times. This study also found that 23.5 percent of men who found employment off their farms were commuters who lived on farms but held regular off-farm jobs. Of these commuters, 41 percent held jobs in factories or mining; most of the rest worked in small enterprises, in communication and transport, or as public officials and teachers. The remaining 15.5 percent of men finding off-farm work were long-term employees, living away from the farm but retaining a close budgetary connection with their farm homes. Long-term workers held roughly the same kinds of job as commuters, but more worked as clerks and in factories, and fewer worked in mining. Of women finding off-farm work, a greater percentage worked as commuters and long-term employees; fewer were seasonal workers. Employment patterns were roughly the same for women as for men, but a somewhat higher percentage of women worked in factories and handicrafts. The study also found that off-farm employment varied considerably from region to region, depending upon the proximity of industrial areas and the availability of factory work, other nonfarm employment, and jobs in the service trades. Industry grew not only in the big cities, but in 62 ECONOMIC GROWTH AND INCOME DISTRIBUTION, 1953-64

Table 2.13. Composition of Off-farm Employment of "Moved-out" Workers, by Type of Work, 1963 (percent)

Seasonal Long-term Commutersa workersb employees'

Type of work Male Female Male Female Male Female

Farming 1.6 2.1 79.6 80.1 2.5 2.0 Mining 14.4 10.5 3.9 3.5 2.1 1.5 Factory labor 27.1 31.9 3.1 4.2 30.5 29.1 Small enterprise 9.0 6.8 - - 6.6 5.2 Clerks 1.1 2.1 - - 12.8 11.9 Public officials and teachers 27.5 24.1 - - 21.1 18.0 Communication and transport 7.6 6.0 - - 7.9 5.8 Handicrafts 1.6 7.0 0.9 1.3 5.0 5.5 Carpenters and plasterers 4.4 3.3 3.4 2.8 4.1 2.9 Other 5.7 6.2 9.1 8.1 7.4 18.1

All workers surveyed 23.5 35.0 61.0 41.1 15.5 23.9

- Notapplicable. Source: Y. C. Tsui and T. L. Lin, "A Study on Rural Labor Mobility in Relation to Industrialization and Urbanization in Taiwan," Economic Digest Series, no. 16 (Taipei: iCRR, 1964), pp. 12-16. a. Commuters are persons regularly traveling back and forth from their farm home and receiving a monthly salary. b. Seasonal workers are persons temporarily working for others during their leisure time and receiving daily wages. c. Long-term employees are persons who leave their farm home and work rather permanently in cities or other places. They nevertheless have close connec- tions with their farm home-for example, by remitting earnings. For convenience, students living away from home, military servicemen, and dependents of long-term employees are included in this category. previously rural areas as well. At times, rural roadbuilding and other construction projects were important sources of off-farm employment in many areas.3R Table 2.14 shows the distribution of the growth of establishments

30. JcRR, Rural Progress in Taiwan (Taipei: JcRR, 1955), pp. 83-85. EFFECTS OF GROWTH ON EQUITY 63

Table 2.14. Establishments in Taiwan, by Location, 1951 and 1961

Growth in Percentage number of distribution Number of establish- of establishments, establishments ments, 1951-61b Locationa 1951 (percent) 1951 1961

Cities 2,959 419.8 24.2 21.5 Semiurban cities 1,235 395.2 10.1 8.5 Semiurban prefectures 2,876 490.1 23.6 24.4 Rural prefectures 2,024 562.2 21.5 25.6 Mixed urban, semiurban, and rural prefectures 2,517 458.0 20.6 20.0

All Taiwan 12,211 472.3 100.0 100.0

Note: See table 3.9 in chapter three for figures to 1971. Source: Industrial and Commercial Census of Taiwan (IcCT), General Report, 1971 Industrial and Commercial Census of Taiwan and Fukien Area, 7 (?) vols. (Taipei: ICCT, 1972), vol. 1, table 6. a. Based on DGBAS definitions in 1964. b. Based on number in operation at the end of the year.

in urban, semiurban, and rural areas, based on 1964 DGBAS definitions. Although some semiurban areas may have been rural in 1951, this table nevertheless gives an idea of the spatial distribution and growth of industrial establishments. It reveals that the distribution of establishments in Taiwan was fairly well dispersed in the early 1950s and that the growth of establishments was fairly uniform into the 1960s. Throughout the 1951-71 period the distribution of establishments did not become concentrated in any one area, especially in such large urban centers as Taipei City and Kaohsiung City, where heavy concentrations might have been expected. This spatially dispersed growth pattern enabled farm families almost anywhere in Taiwan to move easily into rural industries that were intensive in labor. What are the conclusions to be drawn? As a result of rapidly increasing agricultural productivity, Taiwan was able to feed itself and to finance a policy of import substitution on its way to rapid industrialization and successful export substitution. There were 64 ECONOMIC GROWTH AND INCOME DISTRIBUTION, 1953-64

Table 2.15. Gini Coefficients and Factor Shares Based on Income of Urban Wage and Salary Workers, 1955 and 1959

Item 1955 1959

Gini coefficients Total income [Gy] 0.3964 0.3960 Wage income [G.] 0.4210 0.4176 Other income [G,] 0.3162 0.2958

Distributive shares Wage income f+,] 0.7637 0.8196 Other income [f,] 0.2363 0.1804

Sources: 1955 from Economic Planning Council, "Family Income and Ex- penditure Survey of Wages and Salaries by Income Class, Taiwan Province" (Taipei, n.d.; processed in Chinese); 1959 from idem, "Family Income and Expenditure Survey of City Consumers, Taiwan Province" (Taipei, n.d.; processed in Chinese). three main reasons for this success: the early initiation of land reform, government's subsequent support of agriculture, and the dispersed pattern of nonagricultural growth. The distribution of the income of farm families thus improved as a combined result of the initial distribution of assets and the availability of off-farm employment for poorer rural families, particularly the employment opportunities that stemmed from the policy reforms instituted around 1960.

Urban FID Evidence on the distribution of income for nonfarm or urban families during 1953-64 is much sketchier than that for rural families. Hence the results necessarily are less conclusive. Only two studies investigated the distribution of urban wage income alone during the 1950s, and these give some indication of a slight improvement. The first is a study of wage and salary income for 1955; the second, a study of city consumers for 1959.3' If it is assumed that the wage and salary class and the city consumers are roughly comparable categories, comparison of the Gini coefficients derived from

31. Economic Planning Council, "Family Income and Expenditure Survey of Wages and Salaries by Income Class, Taiwan Province;" idem, "Family Income and Expenditure Survey of City Consumers, Taiwan Province." EFFECTS OF GROWTH ON EQUITY 65 these two surveys may be attempted (table 2.15). The basic conclusion, drawn mainly from the more reliable figures on wage income, must be that the urban FID changed very little. At best it improved only slightly, but it certainly contributed much less than rural FID to the overall increase in equity.

Overall FID

The pattern of overall FID for 1953, 1959, and 1964 shows a striking improvement by almost every measure (table 2.16). In 1953 the Gini coefficient was 0.56, which is comparable to patterns of income distribution now prevailing in Brazil and Mexico. By 1964 the Gini coefficient dropped to 0.33, a level comparable to that of the best performers anywhere.3 2 This substantial decline in overall

32. The quality of the data, particularly for the 1950s, is suspect. Calculation of total personal income in 1953, by aggregating the product of average family income and the number of households in each income group, gives a figure 20 percent lower than that of the national accounts data. A similar calculation found that the 1953 data underestimated the total family income given in the national accounts data by 16.7 percent, but that the 1959 data overestimated total family income by 15.3 percent. The 1964 DGBAS data were found to underestimate total family income by only about 5 percent. Although more than half of Taiwan's population in 1953 was in agriculture, 84 percent of the 1953 sample group came from the more urbanized and indus- trialized areas; 58 percent of that group lived in Taiwan's four largest cities. If rural income was better distributed than urban income, as was seen earlier, any overweighting of urban income may have resulted in a low estimate of total personal income and a high estimate of the Gini coefficient. In turn, although DGBAS data for 1964 did not include an appropriate number of families with income exceeding NT$200,000, the downward bias in the Gini probably is too small to be of much importance. Nevertheless the survey results for the 1950s must be accepted with caution. With respect to the underestimation of FID inequality-the 1964 Gini coefficient based on decile groups is 0.328-households with income exceeding NT$200,000 accounted for only 0.1 percent of the population and 1.15 percent of total income. Even if the income share of these households is increased by 1 percentage point, which almost doubles their income share, and if the 1 percent loss is equally assigned to the first nine decile groups, the Gini coefficient increases by only 3.1 percent to 0.3307. The increase really is not that large. To give an idea of the effect of the underestimation of the Gini coefficient, again for the 1964 data, suppose the income share of the top decile group to be increased by 2, 3, and 4 percentage points. Then the Gini coefficients respectively rise by 6.2 percent, 9.3 percent, and 12.4 percent to 0.3406, 0.3505, and 0.3604. Thus the smaller the population, income share, underestimation of the wealthiest households, or any combination of these elements, the smaller the downward bias of the Gini coefficient. 66 ECONOMIC GROWTH AND INCOME DISTRIBUTION, 1953-64

Table 2.16. Measures of the Equity of the Family Distribution of Income, 1953, 1959, and 1964

Item 1958a 1 9 5 9b 1964C

Distribution of income by percentile of households (percent) 0-20 3.0 5.7 7.7 21-40 8.3 9.7 12.6 41-60 9.1 13.9 16.6 61-80 18.2 19.7 22.1 81-95 28.8 26.3 24.8 96-100 32.6 24.7 16.2

Mean income per household (N.T. dollars in 1972 prices) 22,681 31,814 32,452

Per capita GNP in market prices (N.T. dollars in 1972 prices) 6,994 8,629 10,875

Ratio of income share of top 10 percent to that of bottom 10 percent 30.40 13.72 8.63

Gini coefficient 0.5580 0.4400 0.3280

Sources: 1953 from Kowie Chang, "An Estimate of Taiwan Personal Income Distribution in 1953-Pareto's Formula Discussed and Applied," Journal of Social Science, vol. 7 (August 1956), p. 260; 1959 from National Taiwan University, College of Law, "Report on Pilot Study of Personal Income and Consumption in Taiwan" (prepared under the sponsorship of a working group of National Income Statistics, DGBAS; processed in Chinese), table A, p. 23; 1964 from DGBAS, Report on the Survey of Family Income Expenditure, 1964 (Taipei: DGBAS, 1966); Shirley W. Y. Kuo, "Income Distribution by Size in Taiwan Area-Changes and Causes," in Income Distribution, Employment, and Economic Developmentin Southeast and East Asia, 2 vols. (Tokyo: Japan Economic Research Center, 1975), vol. 1, pp. 80-146. a. Data are based on a sample of 301 families, or a sample fraction of 2/1,000. b. Data are based on a sample of 812 families, or a sample fraction of 4/1,000. c. Data are based on a sample size of 3,000 families, or a sample fraction of 14.6/1,000.

FID during the 1950s can be traced primarily to the rapidly improving rural FID, as noted earlier, and secondarily to the distribution of nonagricultural income, which probably did not worsen and may even have slightly improved. EFFECTS OF GROWTH ON EQUITY 67

As will be more fully and rigorously explained in chapter three, the pattern of industrial growth can affect the family distribution of income through changes in the functional distribution of income. For example, if the wage share goes up because of the adoption of a labor-intensive growth path, the distribution of income will improve, assuming that wage income is better distributed than property income, which it generally is. If the wage share declines because of technological changes that save labor and deepen capital, the distribution of family income will worsen. Between 1951 and 1954, the early period of import substitution, the share of wage income in total income sharply increased from 40.7 percent to 46.2 percent (table 2.17). In ensuing years that share was fairly stable, at least until the onset of policies of export substitution again increased the wage share in the 1960s, especially after commercialization. Given the distortion of relative prices usually accompanying import substitution, Taiwan's achievement of a stable wage share is significant. The chief reasons for this performance are that factor prices were more distorted before 1954 than subsequently and that import substitution policies were relatively mild. If a stable or improving wage share is one precondition for the improved distribution of nonagricultural income, the adoption of a labor-intensive growth path is another. Table 2.18 shows the distribution and growth of the branches of manufacturing in which most nonagricultural growth took place. The data indicate that growth in Taiwan during the 1950s was not focused on the highly capital-intensive industries, as is typical in many LDCS. In fact, the most labor-intensive branches of industry grew at rates well above average. The share in total industrial value added of the seven industries most intensive in labor rose from 10.9 percent in 1954 to 17.6 percent in 1961. The large textile and apparel industry, which still was more labor-intensive than the average for all industry, grew at a slower rate; the tobacco industry, the least labor-intensive, became smaller. In addition, manufacturing in Taiwan was much more labor intensive than in the typical LDC, such as West Pakistan. The labor-intensive bias of manufacturing, the good distribution of industrial assets, the pattern of growth and spatial dispersion of the nmore labor-intensive industries, the relatively mild price distortions-all these factors served to improve the overall distribution of nonagricultural income, or at least prevent its worsening. This performance, together with the rapidly improving rural FID, paved the way for the substantial decline observed in overall FID during 68 ECONOMIC GROWTH AND INCOME DISTRIBUTION, 1953-64

Table 2.17. Distribution of National Income, by Factor Share, 1951-72

National TVage Property Agricultural income incomea incomeb income Year (hundreds of thousands of N. T. dollars)

1951 10,527 4,287 2,636 2,980 1952 14,653 6,250 3,470 4,208 1953 19,542 7,911 4,789 6,096 1954 20,761 9,600 5,240 5,171 1955 24,684 11,309 5,816 6,374 1956 28,079 13,188 6,147 6,961 1957 32,409 14,903 7,490 7,957 1958 35,921 16,614 8,353 8,585 1959 41,592 18,781 10,248 9,684 1960 50,828 23,107 11,083 12,969 1961 57,012 26,089 13,178 14,061 1962 61,524 29,182 14,756 14,114 1963 70,603 32,918 18,028 14,688 1964 84,570 39,085 19,803 18,555 1965 91,559 44,036 20,809 19,385 1966 101,967 49,642 24,069 20,373 1967 118,046 58,873 29,647 20,241 1968 136,074 69,770 32,817 21,231 1969 152,795 79,564 37,119 20,484 1970 179,195 93,534 45,763 22,269 1971 204,816 112,115 54,592 21,421 1972 241,320 132,416 61,323 23,688

Note: Although nonagricultural income is functionally classified into wage and property income, agricultural income is not. This explains why the shares here and later in this volume may add up to something slightly less than one and reflects the unimputed mixed income of urban family unincorporated enterprises and professionals. The consistent decline of the share of agricultural income throughout these years reflects a familiar type of structural change in the transition and will be more formally analyzed in chapter three. The reversal from the trend during 1954 and 1955 is a short, noncyclical phenomenon related to the slack in the economy immediately after the Korean War. Sources: DGBAs, National Income of the Republic of China, 1969 and 1974. a. Wages, salaries, and income of professions. b. Property income and income of other incorporated enterprises. EFFECTS OF GROWTH ON EQUITY 69

Distributive shares Relative of national income share of wage and Wage Property Agricultural property income income income income [0o] 11[4r] [1a] [a/r] Year

0.4072 0.2504 0.2841 1.627 1951 0.4265 0.2368 0.2872 1.740 1952 0.4048 0.2451 0.2153 1.652 1953 0.4624 0.2524 0.2491 1.832 1954 0.4582 0.2356 0.2582 1.944 1955 0.4697 0.2189 0.2479 2.146 1956 0.4598 0.2311 0.2455 1.990 1957 0.4625 0.2325 0.2390 1.989 1958 0.4516 0.2464 0.2320 2.072 1959 0.4546 0.2180 0.2552 2.085 1960 0.4576 0.2311 0.2466 1.980 1961 0.4743 0.2398 0.2294 1.978 1962 0.4662 0.2553 0.2080 1.826 1963 0.4622 0.2342 0.2194 1.974 1964 0.4810 0.2273 0.2117 2.116 1965 0.4868 0.2360 0.1998 2.063 1966 0.4987 0.2511 0.1715 1.986 1967 0.5127 0.2411 0.1560 2.127 1968 0.5207 0.2429 0.1341 2.144 1969 0.5249 0.2568 0.1250 2.044 1970 0.5421 0.2640 0.1036 2.053 1971 0.5487 0.2541 0.0982 2.159 1972

the 1950s. It is not possible to say more than this. The meager quantity and quality of data for the 1950s, especially for factor income, preclude formal decomposition analysis of the type undertaken in subsequent chapters. Instead the estimates should be viewed as orders of magnitude that might explain the marked tendency for the value of the Gini coefficient to decline between 1953 and 1964. But even if the magnitude of FID levels and changes must 70 ECONOMIC GROWTH AND INCOME DISTRIBUTION, 1953-64

Table 2.18. Gross Domestic Product, Employment, Share of Wages in Value Added, and Labor Intensity, by Industry, Various Years

Percentage Percentage distribution Real distribution Employ- of GDP in GDP in of ment in manufacturing 1961 employment 1961 (1954= (1954= Industry& 1954 1961 100) 1954 1961 100)

Furniture 0.85 1.14 249.3 2.01 2.63 187.9 Metal products 1.36 3.06 416.9 4.64 4.53 140.8 Transport equipment 1.70 2.84 311.4 5.92 6.29 153.0 Electrical machinery 1.36 2.26 307.6 1.67 2.93 252.2 Printing 3.22 4.41 255.2 3.39 2.94 124.6 Machinery 1.36 2.72 371.1 4.21 3.71 126.6 Rubber 0.91 1.19 244.0 1.74 1.51 124.9 Leather 0.30 0.29 177.0 0.47 0.33 100.0 Wood 3.91 4.88 231.8 5.75 5.91 147.8 Nonmetallic mineral products 5.88 8.10 256.2 9.65 8.82 131.5 Textiles and apparel 24.26 14.86 114.0 21.92 20.91 137.2 Food 26.84 26.51 183.8 20.66 19.86 138.2 Basic metals 1.94 4.14 396.7 2.06 2.45 171.0 Chemicals 10.98 9.27 158.5 5.74 6.97 174.9 Beverages 0.39 0.58 273.0 1.25 1.99 228.7 Paper 2.59 3.53 264.4 2.11 3.04 206.6 Petroleum 3.73 6.16 307.3 1.10 1.24 162.5 Tobacco 6.00 2.69 83.5 1.58 1.21 110.1

Total manufacturinge 100.00 100.00 186.5 100.00 100.00 143.2

n.a. Not available. Sources: GDP figures from DGBAS, National Income of the Republicof China, 1969;employment and labor intensity figures from ICCT,1961 Industrial and Commercial Census; wage figures from Mo-huan Hsing, Taiwan and the Philippines-Industrialization and Trade Policies (London: Oxford University Press for the OECD Development Centre, 1971). a. Ranked by labor intensity in 1954. b. Number of employees per hundred thousand N.T. dollars. c. Includes a miscellaneous category equal to 2 percent of total manufacturing. be taken with a grain of salt, the evidence that a substantial improvement occurred during the 1950s is conclusive. This improvement occurred against the background of an unusually good initial EFFECTS OF GROWTH ON EQUITY 71

Share of wages in value added

Taiwan West Labor Pakistan, intensity 1952 1957-60 1965-68 1967-68 in 1 954b Industrya

n.a. n.a. n.a. n.a. 165.95 Furniture 81.7 63.4 60.7 31.1 122.10 Metal products Transport n.a. n.a. n.a. n.a. 84.66 equipment 58.3 70.7 49.0 29.3 79.18 Electrical machinery n.a. n.a. n.a. n.a. 77.82 Printing n.a. n.a. n.a. n.a. 59.96 Machinery n.a. n.a. n.a. n.a. 57.64 Rubber n.a. n.a. n.a. n.a. 55.96 Leather 71.1 63.7 80.9 43.6 55.39 Wood Nonmetallic mineral 61.2 60.6 56.0 19.9 49.00 products 63.1 53.8 51.3 34.6 44.53 Textiles and apparel 81.1 43.5 58.4 19.1 28.97 Food n.a. n.a. n.a. n.a. 22.90 Basic metals 55.4 49.6 42.6 19.0 19.76 Chemicals n.a. n.a. n.a. n.a. 18.35 Beverages 70.3 58.1 60.0 52.4 13.48 Paper n.a. n.a. n.a. n.a. 9.44 Petroleum n.a. n.a. n.a. n.a. 7.57 Tobacco

n.a. n.a. n.a. n.a. 35.91 Totalmanufacturinge

distribution of assets, the relatively mild regime of import substitution, the efficient use of abundant labor, and the early attention to the rural sector-all of which must have contributed to equity. Furthermore the general liberalization of the economy under the reforms of the early 1960s could only serve to reinforce these trends. More precise analysis linking growth and income distribution nevertheless had to await the superior data that began to become available in 1964. CHAPTER 3

Growth and the Family Distribution of Income by Factor Components

THE DETAILED HOUSEHOLD SURVEY DATA available after 1964 make it possible to move beyond the descriptive treatment of the 1950s and early 1960s to a more analytical assessment of the relations between growth and the family distribution of income (FID) for the 1964-72 period. As mentioned earlier, the total income pattern of n families [Y = (Y1, Y2, ... , Y,)] has a finite number [r] of factor income components [Wi = (Wi, W2, ... , W') (i = 1, 2, ... , r)]. Total income [Y] is the vector sum of such factor income components [Wi] as wage, property, and transfer income. When the labor force is heterogeneous-differentiated by age, sex, skill, and level of education-the wage component is in turn the additive sum of a number of homogeneous wage-income components. If some index of the inequality of total income is adopted-say, the Gini coefficient [G,]-it is possible, in addition, to adopt factor Gini coefficients EGJ] that describe the inequality of distribution of factor income. That index of inequality of total income [GJ] can be decomposed into indexes of the inequality of various factor income components [Gj] and traced to tbem. These factor income components can be of several types, depending on the way their inequality relates to and influencesthe inequality of total income. One type of income, what we label as type one income, is distributed less equally than total income; its share increases as the total income of families increases. Another type of factor income, type two income, is distributed more equally than total income; its share decreases as the total income of families increases. A third type

72 GROWTH AND FID BY FACTOR COMPONENTS 73 of income, type three income, decreases absolutely in magnitude as the total income of families increases; this is unlike type one and type two incomes, which increase absolutely as the total income of families increases. Property income typically is a type one income; wage income a type two income; and transfer income a type three income. Because transfer income is insignificant in Taiwan, the empirical analysis of this chapter focuses only on the first two types of income. It should be emphasized that decomposition of income inequality by source or type of income considerably differs from decomposition by type of income recipient, which is far more common. The purpose here is to introduce a basic decomposition equation that links the inequality of total income [Ga] to the inequality of factor incomes [Gi] and to their shares in total income [44]. In essence that equation states that the inequality of total family income is the weighted sum of the inequalities of the factor incomes, uwith one proviso-that negative signs are attached to the type three incomes. The reason is that type three income contributes not to inequality, but to equality. Because type three income does not enter into the analysis of this chapter, the basic decomposition equation is of the following form: G, = rkGi + 02G2 + . . . + kr,Gr.That equation is then applied to the substantive problem of this chapter: analyzing the relations between growth and FID.1 Two recognizable phenomena accompany the successful develop-

1. For a systematic derivation of the decomposition equations used in this chapter, see chapter ten of part two. A self-contained derivation of the same set of equations is in the appendix to John C. H. Fei, Gustav Ranis, and Shirley Kuo, "Growth and the Family Distribution of Income," Quarterly Journal of Economics, vol. 92, no. 1 (February 1978), pp. 17-53. Other decomposition efforts in the literature include the following: N. Bhattacharya and B. Maha- lanobis, "Regional Disparities in Household Consumption in India," Journal of the American Statistical Association, vol. 62, no. 317 (March 1967), pp. 143-61; V. M. Rao, "Two Decompositions of Concentration Ratio," Journal of the Royal Statistical Society, series A, vol. 132, pt. 3 (1969), pp. 418-25; F. Mehran, "De- composition of the Gini Index: A Statistical Analysis of Income Inequality," (Geneva: International Labour Organisation, n.d.; processed); Mahar Mangahas, "Income Inequality in the Philippines: A Decomposition Analysis," World Em- ployment Programme Working Papers, Population and Employment Working Paper, no. 12 (Geneva: International Labour Organisation, 1975); and Graham Pyatt, "On the Interpretation and Disaggregation of Gini Coefficients," Eco- nomic Journal, vol. 86 (June 1976), pp. 243-55. With the exception of Rao, these articles deal with decomposition by homogeneous groups, not by additive income components. 74 GROWTH AND FID BY FACTOR COMPONENTS ment of a dualistic developing economy: labor is gradually reallocated from agricultural to nonagricultural activities; changes in technology and the accumulation of capital affect the absorption of labor and the functional distribution of income. Within this developmental framework the disaggregation of total income L7] into agricultural and nonagricultural income [Ya and Y,] and the disaggregation of nonagricultural income into wage and property income [Y, and Y.] enable analysis of the relations between growth and FID. Changes in the inequality of total income [G,] over time can thus be examined in relation to changing patterns of growth. Specifically the decomposition equation introduced in this chapter enables attributing the changes in G, over time to three effects: a reallocation effect, a functional distribution effect, and a factor Gini effect. The reallocation effect captures the change in the inequality of income caused by changes in the share of agricultural income in total income. A declining share of agricultural income indicates the shift from agricultural to nonagricultural activities-that is, the extent to which the center of gravity has shifted in a dualistic economy. How does this shift affect the distribution of income? It depends, of course, on whether agricultural income is distributed more equally or less equally than total income. If agricultural income is a type one income, less equally distributed than total income, its declining share would contribute to the equality of total income. If it is a type two income, its declining share would contribute to the inequality of total income. The functional distribution effect captures the change in the inequality of income caused by changes in the relative share of wage and property income. Because wage income typically is a type two income, more equally distributed than total income, it would be expected that any increase in labor's relative share would contribute to the equality of total income. Analogously an increase in the share of the less equally distributed property income would contribute to the inequality of total income. The factor Gini effect captures the change in the inequality of total income caused by changes in the inequality of the various factor income components. In essence the equality of total income increases when the equality of a type one or type two factor income component increases. The opposite is true for a type three component. The first section of this chapter summarizes the technique for decomposing total income inequality into factor income inequality. The second section uses this technique to formulate the problem of INCOME INEQTJALITY AND ITS FACTOR COMPONENTS 75

the effects of growth on FID. The third section presents historical data for the 1964-72 period in Taiwan. The fourth and fifth sections respectively trace the quantitative and qualitative effects of groVth on FID.

Income Inequality and Its Factor Components

At first glance it may seem intuitively appealing to regard total income inequality [Gd] as the sum of the weighted factor Ginis [E0Gj] where the weights [Ei] are the distributive shares of factor income in total income. Such a decomposition nevertheless is likely to be misleading. For example, if transfer income [YN] is concentrated among poor families, and especially if the welfare budget is large, the distribution of YN will contribute to the equality of total income, not to its inequality. In addition, other components of factor income can differ in other ways in their relation to the overall distribution of income. The methodological contribution of this chapter centers on the design of a correct decomposition equation that is sensitive to different types of factor income components and that enables tracing changes in GQover time to changing shares of factor income components. This equation is rigorously developed in chapter ten. Let the pattern of total income of n families [Y] be the sum of r nonnegative factor income components [We]:

(3.1a) 1' (Y1 , Y2, .... , Y-); (3.1b) Y= W + W2 + .. + Wr;

(3.1c) Wi= (Wi, 4. Win) > 0; (i = 1, 2, ... ,r)

(3.1d) s= Wi/Y, where (i = 1,2, . . .r, )

(3.1e) Y = (Y1 + Y2 + ... + Y.)/In,

(3.1f) W7 = (W1I + W21+ ... + Wf)/n, and

(3.1g) k1+ + ±2 *+ r = 1L The values of 4i are the distributive shares of the factor income components in national income. In the numerical example given in table 3.1, where n = 5 and r = 3, the three factor income components are wage income [Wj], property income [7rj], and transfer or welfare income [Nj]. Notice 76 GROWTH AND FID BY FACTOR COMPONENTS

Table 3.1. Numerical Example with Three Factor Income Components and with Total Income Arranged in a Monotonically Nondecreasing Order

Wage Property Transfer Total Item incomel incomes income- income

Income patternb Wj ri N, Yj Family 1 3 (2) 0 (1) 8 (4) 11 (1) Family 2 1 (1) 0 (2) 12 (5) 13 (2) Family 3 17 (5) 2 (3) 0 (3) 19 (3) Family 4 15 (4) 8 (4) 0 (2) 23 (4) Family 5 9 (3) 25 (5) 0 (1) 34 (5)

Total factor income 45 35 20 100

Factor share [oil 0.45 0.35 0.20 1.00

Factor or total Gini [Gi] 0.3912 0.6628 0.6400 0.2239

Estimated income pattern, *o fr lv Yj Family 1 5.79 (1) -2.96 (1) 8.18 (5) 11.00 (1) Family 2 6.50 (2) -0.75 (2) 7.25 (4) 13.00 (2) Family 3 8.64 (3) 5.89 (3) 4.46 (3) 19.00 (3) Family 4 10.07 (4) 10.32 (4) 2.61 (2) 23.00 (4) Family 5 14.00 (5) 22.50 (5) -2.50 (1) 34.00 (5)

Total factor income 45 35 20 100

Factor share [oi] 0.45 0.35 0.20 1.00

Factor or total Gini [Gi] 0.1777 0.7083 0.5202 0.2239

Source: Constructed by the authors. a. The ranks of families are indicated in parentheses. b. From original data. c. Estimated by linear approximation. in this table that total family income [Yj] is arranged in a monotonically nondecreasing order, satisfying: (3.2)t< 0 yn < Y2 < ... < Yc i (ng and that thpe rank index of each factor incorne component is given. INCOME INEQUALITY AND ITS FACTOR COMPONENTS 77

A highly positive rank correlation is assumed between total income and property income; a highly negative rank correlation between total income and transfer income. This pattern gives rise to an intuitive notion: although the unequal distribution of property income contributes to the inequality of total income, the unequal distribution of transfer income contributes to the equality of total income. The typological distinction among income components is emphasized in this section. Heuristically the total Gini coefficient defined on Y can be estimated in the following manner 2 : (3.3a) GV = V- , where [0.2239 = 0.2800 - 0.0561]

(3.3b) G2@= OWG. + OXG, - kNGN.

E0.2800 = (0.45) (0.39) + (0.35) (0.66) - (0.20) (0.64)] The estimator Gini E[] is the weighted average of the factor Gini coefficients; the distributive shares [Ei] defined in equation (3.1d) constitute the system of weights. Notice that a negative sign is assigned to the transfer income term [ENGN]. This assignment conforms to the idea that certain components of income-those having a large distributive share (tN in this case) and a distribution that is more unequal than that of total income (GN in this case)- contribute to the equality of overall Y and reduce the value of G0.3 In the numerical example the error of estimation [0] is 0.0561, and the degree of overestimation [O/Gj] is about 20 percent. Notice that if a negative sign had not been attached to transfer income- that is, if the following alternative estimator [GV]had been used- the error of estimation would have been larger: (3.4a) GV= GV+ E, where E0.2239 = 0.5360 - 0.3121]

2. The numbers in brackets under equations (3.3a) and (3.3b) are based on the numerical example in table 3.1. 3. The rule about whether a plus or minus sign should be attached to certain types of factor income is presented below. As can readily be seen from the numerical example, the intuitive idea is that a minus sign should be attached to the transfer income because it has a negative rank correlation with total income. The more formal analysis of rank correlations is presented in chapter nine of part two. 78 GROWTH AND FID BY FACTOR COMPONENTS

(3.4b) G, = O.G. + O.GY + kNGN. [0.5360 = (0.45) (0.39) + (0.35) (0.66) + (0.20) (0.64)] For the numerical example the error of estimation associated with G, is 0.3121, and the degree of overestimation [E/G,] is more than 100 percent in this case. Return to the general case of equation (3.1) and fit a system of r linear equations to the original data by the method of least squares:

(3.5a) Wi = bi + atY, where (i = 1, 2, ... ,r)

(3.5b) b + b 2+ .. + b = 0 and

(3.5c) a, + a 2 + ... + ar = 1. These linear approximations give this chapter its methodological character. 4 Applying them to the numerical example gives:

(3.6a) X = -15.143 + 1.1071 Y; [property income on Y] (3.6b) W = 1.857 + 0.3571Y; [wage income on Y]

(3.6c) N = 13.286 - 0.4643Y. [transfer income on Y] The factor income components can then be classified into types by the signs of the regression coefficients [ai] and the regression constants [bij.5 For type one income:

(3.7a) ai 2 0, bi < 0; (a, = 1.1071, b,, = 15.143) for type two income: (3.7b) ai > 0, bi > 0O (a. = 0.3571, b,= 1.875)

4. It should be emphasizedthat these regressionrelations are used for purely descriptive purposes; they are devoid of the usual behavioristic connotations associated with regression lines in economics. Notice that the combination of equation (3.1b) with the ordinary least-squares method directly implies equations (3.5b) and (3.5c). 5. Because the n pairs (W', Y,), (W2', Y2 ), . . ., (W,, Y.) are nonnegative, ai and bi cannot both be negative. INCOME INEQUALITY AND ITS FACTOR COMPONENTS 79 for type three income: (3.7c) ai < 0, bi > 0. (aN = -0.4643, bN = 13.286). As will be shown below, type one income is distributed less equally than total income and concentrated among rich families; type two income is distributed more equally than total income. The distinguishing characteristic of type three income (typically welfare income) is that it decreases absolutely as the family is wealthier. This explains why a minus sign is assigned to the transfer income term [ONGN] in the decomposition of the estimator Gini [v] in equation (3.3b). Transfer income is a type three income and may be viewed as an income distribution equalizer. A generalization of equation (3.3b) is the basic decomposition equation used in this chapter: (3.8a) Gy = Gv- B, where

(3.8b) G, = H, + H2 - H3 , where

(3.8c) H1 = 'fi1G1 +± 2G2 + ... + 4tXrGn1

(summation over r1 type one incomes)

(3.8d) H2 = Or,+lG,1 +2 + ... + 0r,Gr2, and

(summation over r 2 - r1 type two incomes)

(3.8e) H3 = On+1Gn2 +2 + . . + O,G.

(summation over r - r2 type three incomes) The usefulness of equation (3.8b) clearly depends on the small size of the error term Ee].To investigate 0, first decompose Y into r factor income components constructed with the aid of the linear regression lines of equation (3.5a): (3.9a) Y= W+ W 2 + ... + W. ;

(3.9b) ri=(*W f2 * *sW);* (i = 1, 2, . ,r) (3.9c) W bi + ajYj; (i =1, 2, ... ,r; j = 1, 2, ... ,n) (3.9d) 4i = (W + i ± .+. . + W+3/n2. =(WI'+ W' + ... W,) /nY = WVi/Yf [see equations (3.1e) and (3.1f)] The decomposition of Y into estimated patterns of factor income 80 GROWTH AND FID BY FACTOR COMPONENTS is shown in the bottom part of table 3.1. [Notice that the values of oi remain unchanged, which verifies equation (3.9d).] Applying the approximation equation (3.8) to the estimated patterns of factor income gives: (3.10a) G, = &,- 0, where

[0.2239 = 0.2239 - 0] (3.10b) 0 = 0 and

(3.10c) G, = O.tGz + ,G; - ONGN. [0.2239 = (0.45) (0.178) + (0.35) (0.708) - (0.20) (0.520)] Thus the error term [0] in equation (3.8a) vanishes when the linear relation between total income [Y] and each factor income component [EW] is perfect: that is, when equation (3.5) is satisfied. The following theorem can now be stated:

THEoREM 3.1. G, = l71+ H 2 - i3, where

(a) 1 = f 1G(W') + ... + <1 G(WVl)

(b) H2 = 01 +1 G(I"+') + ... + 012G(W*r), and

(C) ff = -r2+iG(172+1) + ... ± k0G(Wf). Comparing equation (3.8) and theorem 3.1 shows that the error term [0] in equation (3.8) can be interpreted as a nonlinearity error. It tends to be small or negligible when the linear correlations between total income [Y] and the factor income components [Wi] are nearly perfect: that is, when the correlation coefficients for type one income and type two income approach one and those for type three income approach minus one. In fact the existence of such high correlations is sufficient for the applicability of the basic decomposition equation (3.8). The major task remaining in this section is to show how theorem 3.1 can be derived. We begin with the following theorem, which is rigorously proved in chapter ten: THEOREM 3.2. For type one income and type two income: (a) G(*i) = (aiAk0)G, = (aiffY/Wi)G., and for type three income: (b) G(W1) = -(ai/4i)G, = -(al/Wi)G, -. The theorem states that the Gini coefficients of the estimated pat- INCOME INEQUALITY AND ITS FACTOR COMPONENTS 81 terns of factor income can be obtained by multiplying the Gini coefficient of total income by the elasticity of the regression lines of equation (3.5) at their mean points. The term ai/oi is the elasticity of the regression lines of equation (3.5) at their mean points [Y, Wi] as defined in equations (3.1e) and (3.1f). Notice that for type three income a negative sign is assigned to the right-hand side of theorem 3.2(b) because the Gini coefficients of estimated factor income [G(1I)] and of total income [G,] and the shares of estimated factor income in total income [0i] are nonnegative. Theorem 3.2 can be verified by substituting values from the numerical example. For property income: (3.11a) 0.708 = (1.107/0.35)0.2239, which implies that a,G, = 0,G(t) or (1.107) (0.2239) = (0.35) (0.708); for wage income: (3.11b) 0.178 = (0.357/0.45)0.2239, which implies that

awG,, = O,G(W) or (0.357) (0.2239) = (0.45) (0.178); and for transfer income:

(3.11c) 0.520 = (-0.464/0.20)0.2239, which implies that

aNG, = -,G(19) or (-0.464) (0.2239) =

- (0.20) (0.520).

Now use theorem 3.2 to prove theorem 3.1. When the implied equalities of equations (3.11a), (3.11b), and (3.11c) are added, equation (3.10c) is obtained by using equation (3.5c). Thus theorem 3.1 is obtained in the general case when all r terms aiG, are added. This result shows that theorem 3.1 follows from equation (3.11). Theorem 3.2 can now help to illuminate the difference between type one income and type two income. Making use of the relation, Wi = bi + aiY, rewrite theorem 3.2(a) as follows: For type one income:

(3.12a) G(Wi) = b + Gu, which implies that G(Wi) > Gv, bi ai;< because ai > 0 and b, < 0; 82 GROWTHAND FID BY FACTOR COMPONENTS for type two income:

(3.12b) G(Wi) +ya GY, which implies that G(Wi) < Gv because ai > 0 and bi > 0. Thus type one income is distributed less equally than total income, and type two income is distributed more equally than total income, as can be readily verified by equations (4.9a) and (4.9b). This pattern is borne out by comparison of the factor Gini coefficients in the numerical example with the overall Gini coefficient of 0.224: the factor Gini of property income, a type one income, is 0.708; that of wage income, a type two income, is 0.178. Further- more equation (3.5a) shows that the share of income attributable to the ith factor is:

(3.13) Wi/Y = bi/Y + ai. Because the regression constants for type one income are less than zero (bi < 0), the share of factor income increases with total income. Similarly, because the regression constants for type two income are greater than zero (b1 > 0), the share of factor income decreases with total income. Property income typically is type one income: wealthier families have absolutely and relatively more of such income than poorer families. Wage income typically is type two income: wealthier families have absolutely more but relatively less of such income than poorer families. Type one, two, and three incomes, as summarized in the summation terms [H1 , H2, and H3 ] in equation (3.8), thus represent decreasing contributions to inequality. When there is no type three income-that is when r equals r 2 - equation (3.8) has a special case:

(3.14a) GC,= 'kiGI+ ¢2G2 + ... + trGr- 0; (3.14b) 0 > 0.

As is shown in chapter ten, the nonlinearity term [0] always is nonnegative-that is, the estimator Gini [0,] always slightly overestimates the true Gini [G,,]. In the empirical application of these formulations to Taiwan, only this case is used because of the virtual absence of type three income. The general case of equation (3.8) nevertheless is methodologically more interesting than this special case because it can take into account factor incomes that GROWTH AND THE DISTRIBTJTION OF INCOME 88 contribute to the equality of FID, as well as those that contribute to its inequality.

Growth and the Distribution of Income

Students of income distribution of course are interested in the forces determining the inequality of income [G,] at any given time, but even more in what may occasion changes in G, over time. The approximation equation (3.14a) derived in the preceding section can be used to analyze two types of forces that affect the value of G, over time, assuming that there is no type three income and that the nonlinearity error is small. First assume a simple one-sector economy in which the two factor income components (r = 2) are capital [K] and labor [L] and the respective distributive shares of those components are 4,. and O.. This simple version of equation (3.8) then reduces to: (3.15a) G = 4,XGX + .G., where (3.15b) k. + 0k = 1. Differentiating equation (3.15a) with respect to time t gives: (3.16a) dG,/dt = D + B, where

(3.16b) D = (Gw - G,)dq5/dt and [functional distribution effect] (3.16c) B = ,,(dGW/dt) + 4,,(dG./dt). [factor Gini effect] Equation (3.16a) attributes the causation of changes in G, over time to two distinct types of growth-relevant effects. The functional distribution effect [D] describes the change in G, caused by changes in the relative shares of capital and labor. The factor Gini effect [B] describes the change in Gu caused by the net effect of favorable or unfavorable changes in the factor Gini coefficients. In this simple world the change in G, may thus be traced in part to changes in the functional distribution of income and in part to changes in the patterns of family ownership of labor, capital, land, and so on. Examination of equation (3.16b) reveals that when wage income is distributed more equally than property income (that is, when G,, < G,.) a change in the functional distribution in favor of labor, indicated by a rise in the distributive share of wage income in total 84 GROWTH AND FID BY FACTOR COMPONENTS income [E]J, will always serve to improve FID. In fact this relation establishes the necessary condition for the notion, usually accepted uncritically, that any change in favor of labor's share in income necessarily improves FID. This analysis of the direction of change in the distributive shares of factor income components can be integrated with development theory. In a developing economy such as Taiwan's, two historical periods can be distinguished in addition to the periods of primary import substitution and primary export substitution: the period before commercialization when labor still was in excess supply; the period after commercialization, or the turning point, when surplus labor has been fully absorbed into productive employment. For these two periods the following relations help to link FID directly to the forces of growth:

RELATrON 3.1. Before the turning point, when the real wage ap- proaches constancy, ,, increases only when the degree of the labor-using bias of innovation (in the manner of Hicks) overwhelms the innovation- intensity effect.6

RELATION 3.2. After the turning point, when the real wage is flexible, k. increases only when there is capital deepening or when innovations are biased in a labor-using direction. The growth equation relevant to analyzing the direction of change of the distributive share of wage income [X] after the turning point is:

(3.17) = (1 -w)n,L -1 + BL-

The term 77,denotes the rate of change of any x per unit of time. The term e is the elasticity of substitution; K/L is the capital-labor ratio; BL is the degree of Hicksian labor-using bias of innovation. This equation can be derived from normal analysis of aggregative production functions.7

6. John R. Hicks, Theory of Wages (New York: St. Martin's Press, 1963), ch. 5. 7. For a fuller exposition and derivation of both these equations, see chapter three (especially table 1 and the appendix to that chapter) in John C. H. Fei and Gustav Ranis, Development of the Labor Surplus Economy: Theory and Policy (Homewood, Illinois: Richard D. Irwin, 1964). The term e used in this chapter coincides with the more conventional definition in the literature, but is the reciprocal of the definition used in the volume just mentioned. GROWTH AND THE DISTRIBUTION OF INCOME 85

If equation (3.17) is substituted in equation (3.16b), the functional distribution effect becomes:

(3.18a) D = [EO(G- - GC)dkw/dt]/ckw (= 0.(G. -Gg),.)

(3.18b) = *.(G. - Gr)E(1 - w)( -1) flEIL, + BL].

Equation (3.18b) shows that, when wages are upwardly flexible after the turning point, FID improves under two conditions: when technology change is biased in a labor-using direction (that is, when BL is greater than zero); when there is overall capital deepening (that is, when f,lL is greater than zero). The reason is that the functional distribution effect definitely is favorable (D < 0) only under these conditions. These conditions are the necessary conditions for an improvement in labor's share (see equation [3.17]).8 Nevertheless, as long as the supply of labor still is unlimited and the real wage consequently is nearly constant, equation (3.17) reduces to the following special form9:

(3.19a) 1,j. = BLE - J(1 - f), which implies that

8. This statement is true for the "normal" case of production complementarity-that is, when e < 1. For the case of production substitutability-that is, when e > 1-it is true when there is capital shallowing (i7KlL < 0) instead of capital deepening. 9. When 71.is zero, the rate of labor absorption is:

rlL = 'I + (BL + J/ELL)

(see Fei and Ranis, Developmentof the Labor Surplus Economy, ch. 3). Substi- tuting:

SielL = -(BL + J)/ELL in equation (3.17) gives:

W.etO - (4'r/eLL) (i (B + J) + B) which can be reduced to equation (3.18) with the help of e = /1ELr (see page 85 in the work just cited). By comparing equations (3.18) and (3.20) it can be seen that the behavior of 4,, is caused by different types of forces before and after the turning point. This difference is traced basically to the fact that employment before the turning point is causally determined by capital accumula tion through labor absorption. After the turning point, capital and labor are symmetrical, and the real wage is endogenously determined. 86 GROWTH AND FID BY FACTOR COMPONENTS

(3.19b) qA, > 0 if and only if BL > J -

with --1 > 0.

Combining equation (3.19a) with equation (3.16b) gives the following form to the functional distribution effect before the turning point:

(3.20) D (G-G)[BLE - J(1 - e)].

Consequently, as long as labor is unlimited, FID is improved and Gv, is reduced when equation (3.19) holds: that is, when technology change in the commercialized sector is sufficiently biased in a labor- using direction to overcome J, the innovation-intensity effect.'" Thus, for a labor surplus economy, a high innovation-intensity effect [J] and a high degree of Hicksian labor-using bias of innovation [BL] always contribute to the elimination of unemployment and the coming of the turning point. The distribution of income may nevertheless get worse when the intensity effect [J (1/e - 1)] overwhelms BL. This result would be reflected in a decline in the distributive share of wage income [Ew]and a rise in the inequality of total income [G,]. After the turning point a higher value of BL, combined with capital deepening, contributes to the improvement of FID. This result would be reflected in a decline in G,, an increase in BL, and an increase in flK/L, the rate of capital deepening. Whether these conditions are met determines whether the Kuznets hypothesis about the inverse U-shaped time path of Gv,is valid. In sumrnmary:

RELATION 3.3 When d4./dt > 0, the functional distribution effect is favorable to FID (D < 0) if and only if G.D< G_. What about the factor Gini effect [B]? A negative B, which would contribute to growing FID equity, can be caused by a change in the patterns of asset ownership of capital, labor, or both. The

10. In the normal case of production complementarity, a high innovation intensity leads to more labor absorption and a lower KIL ratio, decreasing labor's share. Thus a high BL contributes both to employment objectives and FID objectives; a high J contributes to the first objective, but not the second. In the "less normal" case of production substitutability, a high J and a high B, would contribute both to the elimination of unemployment and to the improvement of FID. GROWTH AND THE DISTRIBUTION OF INCOME 87 pattern of family ownership of capital becomes more equal over time (that is, dG,,/dt is less than zero) when lower income families acquire capital assets faster than wealthier families do, as might occur because of higher saving rates or favorable inheritance laws or because of land or capital reform. The pattern of family ownership of labor becomes more equal over time (that is, dG,/dt is less than zero) when lower income families acquire more skilled labor because of their expenditure on education or because of government's provision of education to them. In summary:

RELATION 3.4. The factor Gini effect is favorable to FID (B < 0) when there is a net improvement in the equity of the distribution of any factor income (other than a type three income). One additional source of real-world complexity must be accommo- dated when the foregoing relations are applied to a dualistic LDC, such as Taiwan. This complexity can be traced to the dualistic locational aspect of families and production activities and to the importance of agricultural income. Urban families primarily receive income from nonagricultural production, that is, from wage and property income from urban industry and services. Rural families usually receive income from both agriculture and nonagriculture, that is, merged wage and property income from agriculture and wage and property income from rural industry and services. This additional complexity in the real world is the motivation for treating the whole economy in accord with three models: urban households, rural households, and all households. The decomposition equation (3.16) can be directly applied to urban households. But because the models of all households and rural households also have the additional and important source of agricultural income, the analysis of these two groups must be modified. It is substantially enriched in the process. For nonagricultural production the functional distributive shares of wage and property income will be explicitly treated as above; income from agriculture will not, however, be functionally distinguished. This treatment is based on two considerations, the first practical, the second theoretical. First, in the farm-family type of agricultural activity, property and wage income can be disentangled only by using highly artificial procedures of imputation. Second, the essence of development in the dualistic economy is the gradual reallocation of resources, particularly labor, from agricultural to nonagricultural activities. A declining distributive share of agri- 88 GROWTHAND FID BY FACTOR COMPONENTS

cultural income in total income [¢a] is a proxy for this reallocation. Now modify equation (3.15a):

(3.21a) C,, = t.GW + 40aG, where 44 = 44 +± ; X: ± «a = 1; (3.21b) GC = 44G. + 4GC, where 4' = 4/44; 44 = 44/44; 44 + 44 = 1.

The two functional distributive shares in the nonagricultural sector are 44 and 44; the Gini coefficient of all nonagricultural income is GC.Differentiating the inequality of total income [CG] with respect to time t gives: (3.22a) dGC/dt = R + D + B, where

(3.22b) R = (GC- G)da/dt; [reallocation effect]

(3.22c) D = (GC - Gr) (doI/dt)4O; and [functional distribution effect] (3.22d) B = (dGC/dt)Oa + (dCW/dt)o4 + (dCr/dt)o_ [factor Gini effect] The functional distribution effect, which reflects the importance of capital intensity and technology change, can now be summarized by using the shares of wage and profit income from all nonagricultural activity [E4 and 44]. Equation (3.21b) indicates that these shares move in the same direction as the distributive share of wage income [O.] in total income. Thus the entire foregoing discussion of the one-sector case continues to hold in the more complex case. The factor Gini effect remains unchanged, but it now includes agricultural income. What is new is the addition of the reallocation effect [R], which reflects the continuous shift of the economy's center of gravity from agriculture to nonagriculture. A decline in the distributive share of agricultural income in total income is a proxy for this shift. Notice that when such reallocation takes place over time, the distributive share of agricultural income in total income declines over time (d44/dt is less than zero). Thus the impact of the reallocation effect on the equity of distribution of total income [G,] in equation (3.22b) depends upon the sign of the term, GC - GC: that is, on whether the inequality of agricultural GROWTHAND THE DISTRIBUTIONOF INCOME 89 income is greater or less than the inequality of nonagricultural income. When agricultural income is a type two income-that is, when the inequality of agricultural income [Ga] is less than the inequality of total income [G,]-the inequality of nonagricultural income [G.] must be greater than G,. Hence the term, Ga -G, would be negative. As a result, R would be greater than zero, which means that the reallocation effect would cause the overall equity of income distribution to worsen. Conversely, when agricultural income is a type one income-that is, when the inequality of agricultural income [Ga] is greater than the inequality of total income [G ]-it is more of a disequalizer of FID than nonagricultural income. Hence, the term, G. - G., would be positive. As a result, R would be less than zero, which means that the reallocation effect would help to improve overall FID. In summary: RELATION 3.5. When d(a/dt < 0, the reallocation effect is favorable to FID (R < 0) if and only if Ga > G,. Changes in the inequality of total income [Ga] may thus be traced to three forces. The first is the continuous reallocation of labor from agricultural to nonagricultural activities, proxied by the decline of the share of agricultural income in total income as the economic center of gravity shifts from agriculture to nonagriculture. The second is the changing impact of the functional distribution of income as traced to such factors as capital accumulation, technology change, and population growth. The third is the impact of changes in factor income distribution as traced to abrupt changes in asset structure arising from land reform and inheritance laws and to gradual changes arising from different patterns of private and public saving for the formation of physical and human capital. For the first two forces the link of growth theory to FID is quite direct. For the third force the relation of traditional economic analysis to FID is more indirect and complicated. Decomposition equation (3.22), by capturing the effects of these three forces, provides a framework for analyzing the impact of growth on FID in a typical developing economy. It enables us to make qualitative statements about the direction of the impact of a selected pattern of growth on the distribution of income. Moreover it enables us to make quantitative statements about the relative importance of various effects as they contribute to changes in income inequality over time. 90 GROWTH AND FID BY FACTOR COMPONENTS

Empirical Application to Taiwan

Sample survey data on household income in Taiwan-collected by the Directorate-General of Budget, Accounting, and Statistics (DGBAS) for 1964, 1966, 1968, 1970, 1971, and 1972-have been processed in accord with the analytical framework presented in the foregoing section.'" The following assumptions were made in trans- forming the raw data into a simplifying three-model framework. First, a category of unallocable miscellaneous income was ignored, as was the agricultural income of urban families. Both were quantitatively small. Second, no account was taken of intersectoral payments, such as the inclusion in rural wage income of the urban income of farmers' daughters. Isolating such payments in the data was impossible. Third, as pointed out before, agricultural income [Ya] was not functionally disaggregated into wage and property shares. For farm-family agriculture, such a separation would have entailed a rather arbitrary imputation procedure. Table 3.2 summarizes the results for all households, urban households, and rural households. Figures 3.1 and 3.2 provide a graphic depiction of these time series. Table 3.3 gives the results of linear regressions for the three models." Comparison of factor shares emanating from the DGBAS surveys and the national income accounts shows that differences generally are quite small: around 2.5 percent (table 3.4). Consequently the survey data used here are fairly reliable as a source of data on income distribution. The regression coefficients [at] and constants [bi] indicate the following findings:

FINDING 3.1a. For all three models property income was a type one income and wage income was a type two income.'3 Hence G,. < G, < G,.

11. DGBAs, Report on the Survey of Family Income and Expenditure, 1964, 1966, 1968, 1970, 1971, and 1972. 12. For reasons already cited, the values of ai do not quite add up to 1; the values of bj to zero. Regressions are based on grouped data classified into decile population groups. 13. The exception is property income of rural households in 1968: when using deciles, it marginally was a type two income; when using more intervals, it was a type one income. EMPIRICAL APPLICATION TO TAIWAN 91

Figure G.1.(ini Coefficients of Total and Factol Incomes, by M1odel, 1964-72 All households

Cr,. ... - - - 0.4 -

G, -_

0.2-

0.1 [' ------0.1~I ~ ~ ~~~~o I

Urban households

0.4 J _ _ _ _

0.3

0.2

0.1 _lI I I I Rural households

0.4 -

0.3

0.2 Gr ------_.

0.1 Before turning point After turning point

1964 1966 1968 1970 1971 1972

-Total income - -Property income --- lWageincome ---- Agricultural income Source: Table 3.2. 92 GROWTH AND FID BY FACTOR COMPONENTS

Table 3.2. Gini Decomposition by Additive Factor Components, 1964-72

Model and variable Notation 1964 1966 1968

All households Total Gini Gv 0.3208 0.3226 0.3260 Wage Gini G 00.2365 0.2697 0.2932 Property Gini G, 0.4487 0.4104 0.4598 Agricultural Gini Ga 0.3543 0.3410 0.1817 Wage sharea 0. 0.4324 0.4760 0.5066 Property share 0, 0.2401 0.2557 0.2777 Agricultural share 0a 0.2754 0.2118 0.1523 Estimated total Gini G, 0.3218 0.3230 0.3278 Nonlinearity error o= - G 0.0009 0.0004 0.0019 Degree of overestimation D, = O/G, 0.0029 0.0013 0.0058

Urban households Total Gini Gv 0.3288 0.3236 0.3296 Wage Gini Gw n.a. 0.2797 0.2732 Property Gini G, n.a. 0.4193 0.4246 Wage sharea Xw 0.5729 0.5925 0.5673 Property share X, 0.3225 0.3218 0.3366 Agricultural share ka 0.0374 0.0217 0.0288 Estimated total Gini n.a. 0.3244 0.3304 Nonlinearity error 0 = G,-Gv n.a. 0.0008 0.0009 Degree of overestimation D, = I/G, n.a. 0.0026 0.0026 Rural households Total Gini G,, 0.3080 0.3200 0.2842 Wage Gini 0w n.a. 0.1933 0.1880 Property Gini Gr n.a. 0.3344 0.2775 Agricultural Gini Ga n.a. 0.3534 0.3372 Wage sharea 0. 0.2134 0.2016 0.3227 Property share 0> 0.1115 0.1000 0.0994 Agricultural share ¢. 0.6468 0.6595 0.5263 Estimated total Gini Gv n.a. 0.3221 0.2862 Nonlinearity error fl = -G,, n.a. 0.0021 0.0020 Degree of overestimation D, = 0/G, n.a. 0.0065 0.0069

n.a. Not available. Sources: Calculated from DGBAS, Report on the Survey of Family Income and Expenditure,1964, 1966, 1968, 1970, 1971, and 1972. a. The relative shares do not quite add up to 1 because the merged category of EMPIRICAL APPLICATION TO TAIWAN 93

1970 1971 1972 Notation Model a-advariable

All households 0.2928 0.2950 0.2897 Total Gini 0.2775 0.2730 0.2604 G. Wage Gini 0.4278 0.4268 0.4235 G, Property Gini 0.0655 0.1109 0.1105 G. Agricultural Gini 0.5454 0.5974 0.5895 w Wage sharea 0.2558 0.2417 0.2577 0r Property share 0.1307 0.1015 0.1027 0. Agricultural share 0.2939 0.2961 0.2907 G Estimated total Gini 0.0011 0.0011 0.0010 f = G ,-Gv Nonlinearity error 0.0036 0.0036 0.0033 D, = 0/Gv Degree of overestimation Urban households 0.2794 0.2794 0.2813 Gv Total Gini 0.2328 0.2403 0.2349 G,, Wage Gini 0.3689 0.3992 0.3874 G, Property Gini 0.6016 0.6500 0.6335 0. Wage sharea 0.3022 0.2680 0.2975 4, Property share 0.0292 0.0262 0.0235 4. Agricultural share 0.2803 0.2865 0.2832 Gv Estimated total Gini 0.0009 0.0017 0.0019 0 Gv - Gv Nonlinearity error 0.0034 0.0059 0.0068 Dv = O/G, Degree of overestimation

Rural households 0.2772 0.2907 0.2844 Gv Total Gini 0.2042 0.2207 0.2378 Gw Wage Gini 0.3607 0.3370 0.3477 G, Property Gini 0.3138 0.3178 0.2983 0G Agricultural Gini 0.3602 0.3572 0.4226 4. Wage sharea 0.1029 0.1224 0.1072 0, Property share 0.4869 0.4523 0.4230 4a Agricultural share 0.2789 0.2917 0.2847 Gv Estimated total Gini 0.0017 0.0010 0.0003 0 = G0 - Gy Nonlinearity error 0.0063 0.0035 0.0009 Dv = 0/Gv Degree of overestimation mixed incomes, which constitute less than 10 percent of the total, was neglected. In addition, the share of agricultural income in the total income of nonfarm households is uniformly small, which conforms to the assumption about the income of urban households. 94 GROWTH AND FID BY FACTOR COMPONENTS

Table 3.3. Regression Results for Decile Income Groups, 1964-72

Model and variable Notation 1964 1966 1968

All households Slope a,,, 0.292 0.375 0.435 a,r 0.364 0.344 0.411 a, 0.296 0.215 0.070 Constant b, 4.191 3.382 2.907 b, -3.694 -2.971 -5.415 b0 -0.608 -0.098 3.358 Correlation coefficient r, 0.979 0.992 0.995 r,, 0.988 0.992 0.993 r, 0.992 0.991 0.902

Urban households Slope a, n.a. 0.474 0.452 a,. n.a. 0.440 0.440 Constant bw n.a. 4.038 5.139 b,. n.a. -4.033 -4.590 Correlation coefficient r,, n.a. 0.987 0.994 n.a. 0.993 0.998

Rural households Slope a, n.a. 0.123 0.183 a,. n.a. 0.107 0.099 a, n.a. 0.712 0.637 Constant b,, n.a. 2.538 4.469 b,. n.a. -0.224 0.005 b. n.a. -1.688 -3.552 Correlation coefficient rw n.a. 0.974 0.918 r,, n.a. 0.989 0.996 r, n.a. 0.998 0.997

n.a. Not available. Sources: Same as for table 3.2.

FINDING 3.1b. For rural households agricultural income was a type one income. Hence Ga > G,,. FINDING 3.1c. For all households agricultural income was a type one EMPIRICAL APPLICATION TO TAIWAN 95

1970 1971 1972 Notation Model and variable

All households 0.495 0.524 0.511 a, Slope 0.391 0.369 0.387 a, 0.025 0.035 0.035 aa 2.326 3.829 4.722 b. Constant -6.333 -6.729 -7.922 b, 4.987 3.508 4.094 bn 0.995 0.992 0.996 r, Correlation coefficient 0.995 0.992 0.996 r, 0.828 0.950 0.951 ra

Urban households 0.474 0.525 0.518 aw Slope 0.422 0.394 0.417 a. 6.605 7.025 7.478 bw Constant -6.168 -7.108 -7.682 b, 0.988 0.993 0.997 r, Correlation coefficient 0.991 0.992 0.999 r,

Rural households 0.238 0.234 0.321 aw Slope 0.149 0.149 0.146 a, 0.551 0.503 0.448 aa 4.318 5.043 5.021 bw Constant -1.629 -1.083 -1.894 b, -2.276 -2.078 -1.250 b, 0.960 0.928 0.973 r, Correlation coefficient 0.958 0.991 0.974 r, 0.998 0.993 0.998 r, income before 1968 (Ga > Gv) and a type two income after 1968 (Ga < GU).14

14. This reversal of type is a complicated phenomenon related to the rapid decline of the relative importance of the merged agricultural income and the very rapid decline of the Gini coefficient of agricultural income. 96 GROWTH AND FID BY FACTOR COMPONENTS

Figure 3.2. Factor Shares, by Model, 1964-72

All households

0.6 - _

0.5 _

0.4

0.3 -~~

0.2 - _

0.1 B ------

Urban households

0.6 -

0.5-

0.4- L I l I

0.3 +…- - -.-. - -

0.2- Before turning point After turning point 0.1

Rural households

0.6-

0.5 ------

0.4 --

0.3 -

0.1…------

1964 1966 1968 1970 1971 1972

- - Property income --- Wage income - Agricultural income

Source: Table 3.2. EMPIRICAL APPLICATION TO TAIWAN 97

Table 3.4. Comparison of Factor Shares from National Accounts and Household Surveys, 1952-72

Share of Share of Share of wageincome propertyincome agriculturalincome House- House- House- hold National hold National hold National Year surveys accounts surveys accounts surveys accounts

1952 n.a. 0.4488 n.a. 0.2491 n.a. 0.3021 1957 n.a. 0.4910 n.a. 0.2468 n.a. 0.2622 1962 n.a. 0.5027 n.a. 0.2542 n.a. 0.2431 1964 0.4561 0.5047 0.2532 0.2557 0.2905 0.2396 1966 0.5045 0.5276 0.2710 0.2558 0.2245 0.2165 1968 0.5409 0.5635 0.2965 0.2650 0.1626 0.1715 1970 0.5860 0.5789 0.2738 0.2832 0.1403 0.1378 1971 0.6350 0.5960 0.2570 0.2902 0.1079 0.1139 1972 0.6205 0.6090 0.2713 0.2820 0.1082 0.1089

n.a. Not available. Note: Because of differencesin definitions, the category of transfers and miscellaneousincome has a different meaningfor the two sources.To facilitate comparabilityof the factor sharesfor wage,property, and agriculturalincome, the sharesin this table are based on a total incomethat excludesthis category. Sources:Calculated from DGBAS, National Income of the Republic of China, 1967 and 1974; and idem, Report on the Survey of Family Income and Expenditure, 1964, 1966, 1968, 1970, 1971, and 1972.

FINDING 3.1d. For all three models there was no type three income.1 5 (Notice that this finding follows from findings 3.la, b, and c.) Thus the special case equation (3.14a) may be used rather than the general case equation (3.8) for all three models. Notice also that the error term [O] in table 3.2 always is nonnegative, verifying expression (3.14b), and that the degree of overestimation [D,]

15. To be precise, a category of so-called transfers, small enough to be neglected, does show up, but it does not decrease absolutely with total family income, as is required for a type three income. This is not to claim that a negligible volume of type three income could not be detected at some more disaggregated level. 98 GROWTH AND FID BY FACTOR COMPONENTS never exceeds 1 percent in any of the three models.'" Consequently the nonlinearity error can safely be ignored in the empirical analysis. As would be expected, the Gini coefficient of property income is larger than the Gini coefficient of total income; the Gini coefficient of wage income is smaller than the Gini coefficient of total income. Furthermore finding 3.1a implies that, as households get wealthier, the share of wage income decreases and the share of property income increases [see equation (3.13)]. This pattern leads to the generally consistent straddling of the total Gini curve by the two factor Gini curves in figure 3.1.17 Findings 3.1b and 3.1c imply that the curve for the agricultural Gini income lies above the curve for the total Gini for rural households; the opposite generally is true for all households (figure 3.1). Thus the share of agricultural income in the total income of rural households increased with total family income: that is, it was a type one income. Consequently income from nonagricultural rural sources, such as rural industry and services, served as an important FID equalizer because it constituted a larger share of the income of poor rural families than of rich rural families [see equation (3.13)]. The same relation was true for all households before 1968. But for all households after 1968 the share of agricultural income began to decrease with total family income: that is, it became a type two income. Wealthier families began to derive a larger proportion of their income from property income than from agricultural income (see finding 3.1a). Consequently agricultural income became an income equalizer: any decline in its distributive share would have resulted in a worsening of FID. The comparative magnitudes of the factor Gini coefficients of findings 3.1a, 3.1b, and 3.1c then lead to the following conclusions:

FINDING 3.2a. The functional distribution effect: In all models a change in the functional distribution of income in favor of labor-that is, d¢,,/dt > 0 equivalent to d,0'/dt > 0-improved the equity of overall FID (see relation 3.3 and finding 3.1 a).

16. This supports the linearity specification. 17. The reader might recall that this relation was established for the expected, not the actual, pattern of factor income. But in view of the almost uniformly high correlation coefficients in table 3.3, a high degree of linearity is indicated, and the relation G. < G,, < G,. is seen to be valid for the actual factor Ginis as well. IMPACT OF GROWTH ON FID: QUANTITATIVE ASPECTS 99

FINDING3.2b. The reallocation effect: A decrease in the share of agricultural income-that is, doa/dt < 0-contributed to the greater equity of FID for: * rural households before and after 1968 (see relation 3.5 and finding 3.1b) * all households before 1968 (see relation 3.5 and finding 3.lc). It contributed to the greater inequity of FID for all households after 1968 (see relation 3.5 and finding 3.lc). These findings considerably simplify the analytical task in the next section.

Impact of Growth on FID: Quantitative Aspects

With GNP growing at more than 10 percent a year, the 1960s were a period of extremely rapid growth in Taiwan. In addition, the levels of the overall Gini coefficient were unusually low. They held in the 0.30 range between 1964 and 1968 and substantially declined thereafter. The substantial decline, particularly in percentage terms, of the Gini coefficient after the turning point when wages began to rise markedly thus seems to reinforce our independent finding that Taiwan reached the end of its labor surplus condition around 1968.18 Such a pattern is consistent with the views of Lewis, Kuznets, and others. But what is much more interesting and not in keeping with the conventional wisdom, the Kuznets effect was almost completely avoided during the period of rapid growth before 1968. The analytical tools developed earlier in this chapter are used here to assess the reasons for the quantitative behavior of the Gini coefficients for rural, urban, and all households. In other words, the general decomposition equation (3.22) is used to trace changes in the Gini coefficients over time to three "causative" factors: the reallocation effect, the functional distribution effect, and the factor Gini effect. Tables 3.5, 3.6, and 3.7 in this section summarize the results. Because of the natural break apparent in the direction of changes in the Gini coefficients around 1968, that year divides the 1964-72 period into two subphases: before the turning point (BTP),

18. John C. H. Fei and Gustav Ranis, "A Modelof Growth and Employment in the Open Dualistic Economy: The Cases of Korea and Taiwan," Journal of Development Studies, vol. 11, no. 2 (January 1975), pp. 32-63. 100 GROWTH AND FID BY FACTOR COMPONENTS

Figure 3.3. Gini Coefficient of Total [ncome, by Mlodel, 1964-72

- All households 0.36 - - -Urban households ------Rural households 0.34 -

0.32 G, - -

0.30 -

0.28 -

0.26- Before turning point After turning point

0.24 _

l l I I I__ i_ _ I _ I 1964 1966 1968 1970 1971 1972

Source: Table 3.2.

and after the turning point (ATP). The magnitudes and percentages of change in the Gini coefficients are shown for each of the three models, as are the estimated total changes in G, based on decomposition equations (3.16) and (3.22). These results make it possible to deduce the relative quantitative contributions of the reallocation effect [R], the functional distribution effect [D], and the factor Gini effect [B]. For a graphic summary see figures 3.3 and 3.4, and 3.5 and 3.6 in the next section. FINDING 3.3a For all households there was a moderate deterioration of FID before 1968 (+0.0052 or +1.6 percent for 1964-68) and a significant improvement after 1968 (-0.0363 or -11.1 percent for 1968-72) .'9

19. In this section, all percentage changes of Ginis refer to actual changes; all percentage changes of effects refer to their percentage contributions toward the total estimated changes in G,,. IMPACT OF GROWTH ON FID: QUANTITATIVE ASPECTS 101

Figure 3.4. Gini Coefficients of Wlage and Property Incomle, by Model, 1964-72

Before turning poiiit After turning point ~~All households 0.50 _ --- Urban households ------Rural household-s

0.40 -

0.35 -

0.30 -

0.25 -

0.20 ------I

1964 1966 1968 1970 1971 1972

Source: Table 3.2.

FINDING 3.3b For rural households there was a significant improvement of FIDbefore 1968 (-0.0358 or -11.2 percent for 1966-68) and virtually no deterioration after 1968 (+0.0002 or +0.1 percent for 1968-72).

FINDING 3.3c. For urban households there was virtually no deterioration in FID before 1968 (+0.0060 or +1.9 percent for 1966-68) and a significant improvement after 1968 (-0.0480 or -14.6 percent for 1968-72). The absolute magnitude of a "significant" change is about ten times larger than a "moderate change," as is apparent in figure 3.1. For a "significant" change the quantitatively dominant causative factors are to be determined. For a "moderate" change it is to be determined whether that change is the result of the stability of all causa- 102 GROWTH AND FID BY FACTOR COMPONENTS

Table 3.5. Changes in the Family Distribution of Income and Their Decomposition, All-households Model, 1964-72

Percentage Total changea changes Nota- Variable tion 1964-68 1968-72 1964-68 1968-72

Total Gini 0, 0.0052 -0.0363 1.6 -11.1

Reallocation effect R - - - - Functional distribution effect D Factor Gini effect B Agricultural Gini Ga -0.1726 -0.0712 -48.7 -39.2 Nonagricultural Gini G. 0.0389 -0.0422 12.8 -12.0 Property Gini GO 0.0111 -0.0363 2.5 -7.9 Wage Gini 0,D 0.0567 -0.0328 24.0 -11.2

- Not applicable. See note a. Source: Calculated from table 3.2. a. Actual changes in G,,, G(,, G,, G,, and G.. The changes do not equal the sum of the three effects for three reasons: decomposition equations (3.16) and (3.22) do not include the quantitatively small, unallocable category of miscellaneous income (for urban households a small amount of agricultural inconmeis also neglected); there is a small nonlinearity error there is a need to make discrete approximations to continuous changes. tive factors or the result of the offsetting effects of positive and negative causative factors. Concentrating first on the all-households model in table 3.5, the major quantitative finding is: FINDING 3.4. For all households the (net) factor Gini effect was the dominant causative factor of change in total G, both before and after 1968. * Before 1968 the highly favorable agricultural Gini effect (-0.0475 or -183 percent) overwhelmed the highly unfavorable nonagricultural Gini effect (+0.0272 or +105 percent) to cause the slight worsening of G, (+ 0.0052 or +1.6 percent for 1964-68). * After 1968 the still favorable agricultural Gini effect (-0.0108 or -30 percent) reinforced the newly favorable nonagricultural Gini effect (-0.0267 or -75 percent) to cause the significant improvement of G, (- 0.0363 or - 11.1 percent for 1968-72). IMPACT OF GROWTH ON FID: QUANTITATIVE ASPECTS 103

Percentage distribution of Total estimated changeb estimated changeb Nota- 1964-68 1968-72 1964-68 1968-72 tion Variable

-0.0259c -0.03560 lOOC lOOC G2, Total Gini

-0.0052 0.0084 -20 24 R Reallocation effect Functional distribution -0.0004 -0.0065 -2 -18 D effect -0.0203d -0.0 3 75d - 7 8 d -105d B Factor Gini effect -0.0475 -0.0108 - 183 -30 Ga Agricultural Gini 0.0272e -O0.0267e 105e - 75e Gz Nonagricultural Gini 0.0027 -0.0101 10 -28 G, Property Gini 0.0245 -0.0166 95 -47 G,,, Wage Gini

b. Based on decomposition equations (3.16) and (3.22). Consequently the values generally differ slightly from those for actual changes and in rare instances may even change sign. c. Equal to the sum of the three effects. d. Equal to the sum of changes in the agricultural and nonagricultural Ginis. e. Equal to the sum of changes in the property and wage Ginis.

Investigation of the possible causes for the pattern of changes in the overall Gini coefficient leads to the conclusion that the nonagricultural Gini EGz] followed a pronounced inverse U-shaped pattern. That is, the actual G. rose by 12.8 percent in the four years before the turning point and declined by 12 percent in the four years after the turning point. It nevertheless was consistently overwhelmed by the combination of a highly favorable agricultural Gini effect, a moderately favorable reallocation effect, and a slightly favorable functional distribution effect. The result was that the Gini coefficient of total income [G5 ] increased by a mere 1.6 percent before 1968. After the turning point that signaled the end of the labor surplus condition, the nonagricultural Gini effect became highly favorable and was reinforced by the still highly favorable agricultural Gini effect and an even more favorable functional distribution effect. These effects overwhelmingly offset the unfavorable reallocation effect. The reason is that once a lot of labor had been reallocated 104 GROWTH AND FID BY FACTOR COMPONENTS

Table 3.6. Changes in the Family Distribution of Income and Their Decomposition, Rural-households Model, 1966-72

Total changes Percentagechanges Nota- Variable tion 1966-68 1968-72 1966-68 1968-72

Total Gini Gy -0.0358c 0.0002 -11.2e 0.1

Reallocation effect R - - - Functional distribution effect D Factor Gini effect B - - - - Agricultural Gini Oa -0.0162 -0.0389 -4.1 -11.5 Nonagricultural Gini GD -0.0310 0.0509 -12.9 24.3 Property Gini G,r -0.0569 0.0702 -17.0 25.3 Wage Gini G,. -0.0053 0.0498 -2.7 26.5

- Not applicable. See note a to table 3.5. Note:It should be recalledthat the data do not permit a detailed factor decomposition for rural householdsfor 1964. Consequentlythe decompositionresults are for 1966onward. Source:Calculated from table 3.2. a. See note a to table 3.5. by 1968, agricultural income switched from being a type one income for all households to a type two income. Consequently the weight of agriculture was reduced, and it no longer served as an FID equalizer. The result was that FID showed a highly significant improvement: the overall G, declined by 11.1 percent in the short span of four years. The combination of these effects led to the very mild Kuznets effect observed for the overall time pattern of G,. All this evidence implies that the Kuznets effect is a complex phenomenon that needs to be disaggregated. In its extreme form, it really is relevant only to the nonagricultural sector. In countries where agricultural activity is important-as it is in Taiwan and in most LDCs-growth does not necessarily conflict with equity, even before the turning point has been reached.2 0

20. This observed, mild, overall Kuznets effect could also be examined in relation to the partially offsettingtime patterns of the Ginis, taken separately, of urban and rural households(see figure 3.3 below). Before the turning point IMPACT OF GROWTH ON FID: QUANTITATIVE ASPECTS 105

Percentage distribution of Total estimated changeb estimated changeb Nota- 1966-68 1968-72 1966-68 1968-72 tion Variable

-0.03 6 7d -0.0120d lOod lOOd Gu Total Gini

-0.0151 -0.0133 -41 -111 R Reallocation effect Functional distribution -0.0041 -0.0013 -11 -11 D effect -0.0175e 0.0026e -48e 22e B Factor Gini effect -0.0107 -0.0205 -29 -171 Ga Agricultural Gini -0.0068f 0.0231f -19f 193f G. Nonagricultural Gini -0.0057 0.0070 -16 59 G,. Property Gini -0.0011 0.0161 -3 134 Gt Wage Gini

b. See note b to table 3.5. c. Comparable figures for 1964-68 are -0.0238 and -7.7 percent. d. Equal to the sum of the three effects. e. Equal to the sum of changes in the agricultural and nonagricultural Ginis. f. Equal to the sum of changes in the property and wage Ginis.

FINDING 3.5. For rural households the favorable reallocation effect had a quantitative significance almost equal to or greater than that of the factor Gini effect. , Belfore 1968 the favorable reallocation effect (-41 percent) reinforced the favorable factor Gini effect (-48 percent) to cause the significant improvement of GQ (-0.0358 or -11.2 percent for 1966-68). * After 1968 the highly favorable reallocation effect (-111 percent) overwhelmed the unfavorable factor Gini effect (+22 percent) to cause the very modest deterioration of Gr, (+0.0002 or -0.1 percent for 1968-72).

the favorable FID trend for rural households tends to offset the slightly unfavorable FID trend for urban households; after the turning point the opposite is true. This approach relates more to the method of segmentation of total family income by homogeneous groups, as suggested by Theil-a method which is more difficult to link directly to growth-related phenomena. Henri Theil, Statistical Decomposition Analysis (Amsterdam: North-Holland, 1972). 106 GROWTH AND FID BY FACTOR COMPONENTS

Table 3.7. Changes in the Family Distribution of Income and Their Decomposition, Urban-households Model, 1966-72

Total changea Percentagechangea Nota- Variable tion 1966-68 1968-72 1966-68 1968-72

Total Gini a7, 0.0060c -0.0480 1 .9c -14.6

Reallocation effect R - - Functional distribution effect D - - - - Factor Gini effect B

Agricultural Gini - - - Nonagricultural Gini G, -0.0007 -0.0460 -0.2 -14.0 Property Gini Gr 0.0053 -0.0372 1.3 -8.8 Wage Gini Gw -0.0065 -0.0383 -2.3 -14.0

- Not applicable. See note a to table 3.5. Note: It should be recalled that the data do not permit a detailed factor decomposition for urban households for 1964. Consequently the decomposition results are for 1966onward. Source: Calculated from table 3.2.

Thus the reallocation effect is quantitatively most important for rural households simply because of the greater share of agricultural income in the total income of those households. The favorable impact of the reallocation effect (-41 percent) before the turning point was consistently reinforced by the factor Gini effect (-48 percent) and the functional distribution effect (-11 percent). The consistently favorable impact of all three effects thus gave rise to a substantial improvement in rural FID before the turning point: the inequality of rural income [Gv] declined by 11.2 percent during 1966-68. For the 1968-72 period after the turning point, the nonagricultural Gini increased by 24.3 percent; the agricultural Gini declined by 11.5 percent. This pattern reduced the importance of the factor Gini effect to 22 percent, but by this time it was unfavorable to FID. It nevertheless was overwhelmed by the increased importance of the still favorable reallocation effect (-111 percent) and the still favorable functional distribution effect (-11 percent). Consequently there was almost no worsening of rural FID. The inequality of rural income (G,,) increased by only 0.1 percent. IMPACT OF GROWTH ON FID: QUANTITATIVE ASPECTS 107

Percentage distribution of Estimated changeb estimated changeb Nota- 1966-68 1968-72 1966-68 1968-72 tion Variable

d 100d Gini 0. 0 0 13d -0.0442d 1 0 0 G, Total

- - - - R Reallocation effect Functional distribution 0.0035 -0.0100 269 -23 D effect -0.0022e -0.0342e - 169e -77e B Factor Gini effect

- - - G, Agricultural Gini -0.0022 -0.03421 -169f -77f Gz Nonagricultural Gini 0.0017 -0.0125 131 -25 0G,, Property Gini -0.0039 -0.0217 -300 -49 GC, Wage Gini

a. See note a to table 3.5. b. See note b to table 3.5. c. Comparable figures for 1964-68 are -0.0008 and 0.2 percent. d. Equal to the sum of the two effects. e. Equal to the nonagricultural Gini. f. Equal to the sum of changes in the property and wage Ginis.

FINDING 3.6. For urban households the functional distribution effect had a quantitative significance greater than or almost equal to that of the factor Gini effect. * Before 1968 the highly unfavorable functional distribution effect (+269 percent) overwhelmed the moderately favorable factor Gini effect (-169 percent) to cause the m.oderate worsening of Gv ( + 0.0060 or + 1.9 percent for 1966-68). - After 1968 the moderately favorable functional distribution effect (-23 percent) reinforced the favorable factor Gin-i effect (-77 percent) to cause the significant improvement of G' (-0.0480 or -14.6 percent for 1968-72).

Analysis of the pattern of urban FID alone shows that the time pattern of the functional distribution effect reflects the time pattern of the inequality of urban income [G2]. The functional distribution effect is important to the pattern of distribution of urban household income because, as seen in the foregoing discussion, the main forces 108 GROWTH AND FID BY FACTOR COMPONENTS affecting changes in the share of nonagricultural income in the total income of urban households are capital deepening and technology bias and intensity. The highly unfavorable functional distribution effect before the turning point was softened by the very favorable factor Gini effect, which moderated any worsening of urban FID. The net result was that the inequality of urban income [Gu] increased by only 1.9 percent during 1966-68. With the exhaustion of surplus labor after the turning point, the functional distribution effect became favorable to urban FID. The newly dominant and still favorable factor Gini effect (-77 percent) reinforced the newly favorable functional distribution effect (-23 percent). Consequently urban FID tremendously improved. The inequality of urban income [Ou] declined by 14.6 percent. These time trends lead to a time pattern of urban FID that is slightly inverse U-shaped. The reader may have noted some diffidence in the interpretation of the empirical evidence in this section. The reasons are these: Slight changes in the magnitude of the Gini coefficient do not war- rant stronger statements in the absence of statistically designed tests of significance. In the pioneering field of analyzing the distribution of income, reliable methods for assessing the significance of variations in data do not yet exist. It must thus be candidly admitted that quantitative findings rely for some of their strength on qualitative findings based on heuristic judgments about their significance in relation to growth.

Impact of Growth on FID: Qualitative Aspects

In this section the findings about the impact of growth on FID are further analyzed and interpreted in relation to the reallocation effect, the functional distribution effect, and the factor Gini effect. First the changes in the total and sectoral Gini coefficients are described. Then the impact of the reallocation effect, functional distribution effect, and factor Gini effect on these underlying phenomena are further analyzed on the basis of findings in the preceding section. The theoretical underpinnings of this analysis are discussed in chapter eleven.

The pattern of Gini coefficients over time The following statements can be made about the behavior of the Gini coefficients for all households, rural households, and urban IMPACT OF GROWTH ON FID: QUALITATIVE ASPECTS 109 households during the 1964-72 period:

FINDING 3.7a. For all households G, increased slightly between 1964 and 1968, but consistently and markedly declined thereafter.

FINDING 3.7b. For urban households Gu showed the same time pattern as that for all households, but was slightly more pronounced.

FINDING 3.7c. For rural households G' significantly declined between 1964 and 1968, but remained relatively constant thereafter.

These observations underscore the arrival of the turning point in the family distribution of income at some time around 1968. We consider this conclusion to be highly significant in the light of our previous work on Taiwan: as was indicated in chapter one, the period around 1968 was independently established as something of a landmark in Taiwan's development path.2 1 That year marked the end of labor surplus and the beginning of labor scarcity. It is interesting to note, for all households and urban households, that the distribution of income improved once conditions of labor scarcity arrived and real wages began to rise sharply. Of greater importance, however, is the observation that FID did not worsen very much for any of the three models, even during the period of unusually rapid growth in the early and mid-1960s. As already noted, the Kuznets effect is a complex phenomenon mainly relevant to the nonagricultural sector. Examination of the comparative magnitudes of the urban and rural Gini coefficients provides additional insights about this phenomenon.

The comparative magnitudes of total and sectoral Gini coefficients How do the sectoral Gini coefficients for rural and urban households compare with the total Gini coefficient for all households?

FINDING 3.8a. Before the turning point the urban Gini [G ] was greater than the overall Gini [G5 ], which was greater than the rural Gini [Gv].

21. See Fei and Ranis, "Model of Growth and Employment," and Mo-huan Hsing, Industrialization and Trade Policies: The Case of Taiwan (London: Ox- ford University Press for the OECD Development Centre, 1971). 110 GROWTH AND FID BY FACTOR COMPONENTS

FINDING 3.8b. After the turning point the overall Gini [G5 ] was greaterthan the rural Gini [GQ],which generallywas greaterthan the urban Gini [Gu]. Finding 3.8a implies that industrialization was more rapid in urban centers. Consequently the extent of urban dualism was greater than its rural counterpart before the turning point: the concentration of assets was more substantial; the variations in the scale of production and heterogeneity of labor were wider. Furthermore, despite the substantial inequality of the distribution of agricultural income among rural households, the inequality of rural income [G6] was less than the inequality of urban income [EG]. This pattern suggests that modernization and nonagricultural activity had not yet reached rural areas in a big way. After the turning point-that is, by 1971-the inequality of rural income [EG] became larger than the inequality of urban income [EG6](see figure 3.3a). Finding 4.17 thus implies that rural areas caught up with urban areas in their degree of modernization and their concomitant rise in structural dualism and FID inequality 2 2 just when the effect of urban dualism on FID was declining. Additional data on the inequality of income [G,] for all households in 1964 and 1968, broken down by urban, semiurban, and rural location, can be used to explore further this issue of how and when modernization occurred (table 3.8) .23 For all households in both years, the results show that the inequality of urban income was greater than the inequality of semiurban income which, in turn, was greater than the inequality of rural income. In addition, the inequality of nonfarm income in the three locations was greater than the inequality of farm income. This evidence implies that, in

22. Because the sectoral Ginis in figure 3.3 are smaller than the total Gini, intrasectoral income inequality is less than intersectoral inequality. In the terminology of the Theil index, the large G%is the result of the strength of intergroup income variations, not intragroup income variations. See Theil, Statistical Decomposition Analysis. 23. The rural and urban breakdowns, available only for these two years, refer to the precise location of households and therefore are not exact equivalents of the "rural" and "urban" categories, which earlier were used generally and which include small amounts of semiurban dwellers. The urban households are almost exclusively nonfarm households, as are the great majority of semiurban households. Most rural households are farm households. Also see finding 3.2. IMPACT OF GROWTH ON FID: QUALITATIVE ASPECTS 111

Table 3.8. Gini Coefficients Based on Decile Population Groups for Urban, Semiurban, and Rural Households, 1964 and 1968

Percent- age Share of Share of Gini change households income coefficient in Gini Categoryof coefficient, household 1964 1968 1964 1968 1964 1968 1964-68

Non!farmand farm households All households 1.0000 1.0000 1.0000 1.0000 0.3208 0.3259 1.59 Urban households 0.3000 0.3243 0.3473 0.4348 0.3185 0.3230 1.41 Semiurban households 0.3435 0.3245 0.3381 0.2852 0.3175 0.3119 1.76 Rural households 0.3565 0.3332 0.3146 0.2800 0.3115 0.2940 -5.62

Nonfarm households All households 1.0000 1.0000 1.0000 1.0000 0.3288 0.3296 0.24 Urban households n.a. 0.4819 n.a. 0.5625 n.a. 0.3259 n.a. Semiurban households n.a. 0.3119 n.a. 0.2732 n.a. 0.3135 n.a. Rural households n.a. 0.2063 n.a. 0.1643 n.a. 0.3022 n.a.

Farm households All households 1.0000 1.0000 1.0000 1.0000 0.3080 0.2842 -7.73 Urban households n.a. n.a. n.a. n.a. n.a. n.a. n.a. Semiurban households n.a. 0.3519 n.a. 0.3214 n.a. 0.2817 n.a. Rural households n.a. 0.6088 n.a. 0.6303 n.a. 0.2863 n.a.

n.a. Not available. Note: The urban, semiurban, and rural categories of household are based on the classification used by the DBGAS in its household surveys. The categories are not to be confused with the categories "urban" and "rural" (which include semiurban dwellings) used elsewhere in this volume. Sources: Calculated from DGBAS, Report on the Survey of Family Income and Expenditure, 1964 and 1968.

moving from urban to semiurban to rural areas, the degree of modernization and the inequality of FID decrease. Thus modernization probably occurs first in the largest urban centers and then slowly permeates semiurban and rural areas. Because the original urban-households model includes a small proportion of semiurban and rural households, the results given in 112 GROWTH AND FID BY FACTOR COMPONENTS table 3.8, disaggregated into urban, semiurban, and rural households, can also be used to refine the test of the relevance of the Kuznets hypothesis to the nonagricultural sector. Between 1964 and 1968 the GQ for urban households worsened; that of rural households improved. Further comparison shows that the change in the GD for urban households, which earned all their income from nonagricultural sources, was much larger than that for all nonfarm households. Thus the observed worsening of the overall GQ was mostly the result of the Kuznets effect of modern urban nonagricultural activity on FID. Nevertheless, even where FID worsened because of the Kuznets effect, that worsening was so mild as to be insignificant. The nonfarm Gini increased by 0.24 percent; the purely nonagricultural urban Gini increased by 1.41 percent. But this worsening of urban FID was ameliorated by corresponding improvements in the semiurban Gini and the rural Gini. Conse- quently the Kuznets effect on the overall G, was very mild. This pattern suggests two conclusions. First, the more that nonagricultural activity is urban-centered, the more the Kuznets effect is significant. Second, where agricultural activity is important and industrialization is decentralized, as they are in Taiwan, growth need not conflict with FID, even before the turning point. Throughout the eight years under observation, the level of the Gini coefficient is unusually favorable, certainly by LDC standards, and it appears that things really do not have to get worse before they can get better. Because this result flies in the face of much general empirical evidence for postwar LDcs, as well as the theoretical arguments of Lewis, Kuznets, and others, it should be of considerable interest to see what emerges from an attempt to dig a little deeper into the causation of changes in FID with the help of tools developed earlier in this chapter. In summary, our evidence does support the existence of a close relation between growth and FID, with marked improvements in FID after the turning point, as we might have suspected, but without any marked deterioration before, as we might not have suspected. We will now explore these issues further, with particular attention to the three types of effects we have identified.24

24. The mildness of the Kuznets effect, coupled with the low level of G, by international standards, was a major motivation for this study. See for example Hollis Chenery and others, Redistribution with Growth (London: Oxford Uni- versity Press, 1974). IMPACT OF GROWTH ON FID: QUALITATIVE ASPECTS 11I

The reallocation effect As already noted, the shift of the economic center of gravity from agricultural to nonagricultural activities, a reallocation effect proxied by the declining share of agricultural income in total income, clearly is a critical feature of development in the dualistic economy. FINDING 3.9. For rural households and all households the distributive share of agricultural income [4a] consistently declined throughout the entire period. The speed of this shift, whether measured by income generated or labor force, accelerated during the phase of export substitution that began in about 1961.25 During the 1960s Taiwan's nonagricultural labor force increased by a remarkable 80 percent, compared with a rise of 35 percent during the 1950s. The agricultural labor force increased by only 5 percent during the 1950s and 4 percent during the 1960s. In the latter decade the agricultural labor force was partly reallocated to (absorbed by) labor-intensive, export-oriented industries and services in the cities, but partly also to spatially dispersed rural industries and services, which rapidly emerged as an additional source of income for rural families. By the end of the 1960s the share of agricultural labor in the labor force had declined from about a half to only a third. In addition, and of considerable importance, those remaining in the agricultural labor force spent more and more of their time on nonagricultural activities. By 1964, when the DGBAS surveys began, rural industries and services already were important sources of rural family income. They subsequently assumed an even larger role. In 1964 the combined share of rural wage and property income [or + r] in the total income of rural families [YrI was 33 percent; in 1972 it was 53 percent. 2 6

25. Such labor reallocation is well proxied by O.. Although the agricultural labor force has not substantially increased since the beginning of the 1950s, the increase in the total labor force caused the share of the agricultural labor force to decline tremendously. See Shirley W. Y. Kuo, "A Study of Factors Contribut- ing to Labor Absorption in Taiwan, 1954-1971" (paper read at the Conference on Population and Economic Development in Taiwan, December 29, 1975- January 2, 1976; processed). 26. This increase is quite remarkable by any international LDC standard. The relative importance of nonagricultural rural activity can also be seen in its value 114 GROWTH AND FID BY FACTOR COMPONENTS

The steady rise in the nonfarm income of farm families began in the 1950s. The JCRR surveys of farm-family income conducted between 1952 and 1967 show a continuous rise in the distributive share of nonfarm income in total family income from 22 percent in 1952 to 37 percent in 1957, 41 percent in 1962, and 42 percent in 1967.27Moreover the proportion of farm families who considered themselves to be part-time farmers rose from 52 percent in 1960 to 68 percent in 1965 and 72 percent in 1970.28 By 1968 rural by- employment had become the dominant form of rural labor reallocation and the dominant source of rural family income. Although the total agricultural labor force remained relatively constant, the share of agricultural income in total income continued to decline rapidly. Even during the 1950s this steady rise of the share of nonfarm income had considerable importance as an equalizer of rural FID. The surveys of farm-family income conducted by the JCRR show that the poorest families, proxied by those with the least land (less than 0.5 chia), earned 62 percent of their total income from nonfarm sources in 1957, 74 percent in 1962, and 66 percent in 1967. Corre- sponding figures for the wealthiest families, proxied by those with the most land (more than 2 chia), were 25 percent in 1957, 25 percent in 1962, and 26 percent in 1967.29In addition, cross-sectional evidence for 1967 indicates that the proportion of families who considered themselves to be part-time farmers increased as farm

added, which averaged about 20 percent of that of urban industry during the period. See International Labour Organisation (ILO), "Sharing in Development: A Programme of Employment, Equity and Growth for the Philippines," in Special Paper no. 9 on Medium-Scale and Small-Scale Industry (Geneva: ILo, 1974), pp. 539-68. 27. JCRR, "Taiwan Farm Income Survey of 1967-with a Brief Comparison with 1952, 1957, and 1962," Economic Digest Series, no. 20 (Taipei; JCRR, 1970); idem, "A Summary Report of Farm Income of Taiwan in 1957 in Comparison with 1952," Economic Digest Series, no. 13 (Taipei: JCRR, 1959). Because of differences in definitions, the values of the shares differ somewhat from those of the DGIBAs household surveys for the nearest years, 1966 and 1967. The trend nevertheless is unmistakable. 28. Taipei Provincial Government, Committee on the Census of Agriculture, Report of the Census of Agriculture, 1960, 1965, and 1970. 29. Further disaggregation also shows for poorer families that relatively more of that nonfarm income is wage income, not property income. See below for more on the functional distribution of nonagricultural income. JCRR, "Taiwan Farm Income Survey of 1967." IMPACT OF GROWTH ON FID: QUALITATIVE ASPECTS 115 size decreased-from 51 percent of families having more than 2 chia to 84 percent of families having less than 0.5 chia.8 0 The seeds for this rapid shift in the economic center of gravity were planted in the 1950s, when locationally dispersed rural industries began to grow and meet the need and desire for supplementary farm income. Table 3.9 shows the growth and distribution of the number of establishments between 1951 and 1971 grouped into cities, semiurban cities, semiurban prefectures, rural prefectures, and prefectures that are a mixture of urban, semiurban, and rural according to definitions adopted by the DGBAS for the household survey in 1964. This table reveals not only that the initial distribution of nonagricultural establishments was remarkably dispersed in Taiwan, but that growth rates also were quite evenly distributed from 1951 onward.3 ' This table also shows that rural areas enjoyed the highest growth rate over the entire period, a remarkable contrast with the performance of most LDCS. Male labor in rural infrastructure and female labor in home-based handicrafts oriented toward the domestic market exemplified the early forms of nonfarm income. But with the accelerated growth and industrialization of the urban sector and with the new export orientation of government policies in the 1960s, modernization slowly permeated the rural sector. The previously unorganized small handicrafts were organized into small factories, which increasingly modernized in response to export demand.3 2 This industrialization of the rural sector was accompanied by substantial growth in agricultural productivity, especially when high-yielding varieties were superimposed on an already productive and research-oriented agricultural sector. With agricultural productivity rising, farmers could spend more time on nonagricultural activities. Taiwan's experience thus shows that fostering a spatially dispersed industrialization pattern, in addition to being beneficial for growth, is a practical way to improve FID for rural households.

30. Derived from the JCRR farm-family income in Y. H. Yu, "Economic Analy- sis of Full-time and Part-time Farms in Taiwan" (Taiwan Provincial Chung Hsing University, 1969; processed). 31. For example, the three largest cities combined went from 24 percent to 26 percent of total establishments over the twenty-year period. This is in sharp contrast with the growth of establishments in Thailand or the Philippines. 32. Mo-huan Hsing, Relationship between Agricultural and Industrial De- velopment in Taiwan during 1950-59 (Taipei: icmu, 1960); Edward S. Kirby, Rural Progress in Taiwan (Taipei: JCRR, 1955). 116 GROWTH AND FID BY FACTOR COMPONENTS

Table 3.9. Establishmentsin Taiwan, by Location, 1951-71

Number Growth in number of establishmenteb of estab- (percent) lishments Locationa 1951 1951-61 1961-68 1968-71 1951-71

Cities 2,959 419.8 854.2 1,164.3 2,438.3 Semiurban cities 1,235 395.2 755.7 903.4 2,054.3 Semiurban prefectures 2,876 490.1 877.0 861.1 2,228.2 Rural prefectures 2,024 562.2 1,063.6 915.6 2,541.4 Mixed urban, semiurban, and rural prefectures 2,517 458.0 804.7 766.8 2,029.5

All Taiwan 12,211 472.3 884.5 931.0 2,287.8

Source: Industrial and Commercial Census of Taiwan (ICCT), General Report, 1971 Industrial and Commercial Census of Taiwan and Fukien Area, 7 (?) vols. (Taipei: IccT, 1972), vol. 1, table 6. a. Based on DGBAs definitions in 1964. b. Based on number in operation at the end of the year.

What, then, can be concluded about the reallocation effect? FINDING 3.10a. For rural households the reallocation of labor from agricultural activity to rural industries and services improved FID equity throughout the entire period (see finding 3.2b, finding 3.5, and relation 3.5). FINDrNG 3.10b. For all households the reallocation of labor from agricultural to nonagricultural production improved FID equity before the turning point and worsened FID equity after the turning point (see finding 3.2b, finding 3.4, and relation 3.5).

The functional distribution effect Turn now to the functional distribution effect, which is caused by variations in the ratio of the wage share in nonagricultural production to the property share [EW/OT] and hence is a proxy for labor intensity. The time paths of that ratio for all three models are given in figure 3.5. FINDING 3.1 la. The relative share ratio [EO/0,] was higher for rural industries than for urban industries. IMPACT OF GROWTH ON FID: QUALITATIVE ASPECTS 117

Distribution of establishnents (percent)

1951 1961 1968 1971 Location,

24.2 21.5 22.8 25.8 Cities 10.1 8.5 8.6 9.1 Serniurban cities 23.6 24.4 23.7 22.9 Semiurban prefectures 21.5 25.6 25.7 23.9 Rural prefectures Mixed urban, semiurban 20.6 20.0 19.2 18.3 and rural prefectures

100.0 100.0 100.0 100.0 All Taiwan

Figure 3.5. Ratio of the Wage Share in Nonagricultural Production to the Property Share, by Model, 1964-72

Before turning point I After turning point

4.0 - All industries .--- Urban industries ------Rural industries , 3.5-

3a0 - g

2.5-

2.0 - --½' ---& - --

1964 1966 1968 1970 1971 1972

Source: Calculated from table 3.2. 118 GROWTH AND FID BY FACTOR COMPONENTS

Figure 3.6. Ratio of Average Urban Income to Average Rural Income for Wage and Property Income, 1964-72

Beforeturning point After turning point

- - - Property income

------Wage income / -

4 -

3~~~ - -t/r \ /

0 ---.-. ------7~---

1964 1966 1968 1970 1971 1972

Source: Calculated from table 3.2.

FINDING 3.11b. In both rural and urban industries X. exceeded 4,r- that is, or /oJr > +Xue/0 > 1.

Finding 3.11a implies that industrial and service activities, under normal conditions of substitution-inelastic production functions, are more capital intensive in urban areas than in rural areas.3" Figures compiled from the 1961 and 1971 censuses of industry and commerce substantiate the thesis that the ratio X,/+,, is a good proxy for labor intensity (table 3.10). The results indicate, for almost

33. If p is the wage-profit or factor-price ratio applying to both sectors-that is, there are no factor-price distortions-and if K and K* respectively are the capital-labor ratios for rural and urban nonagriculture, the inequality in finding 3.1la implies that p/K* > p/Kr or K* > K*. That is, for the same p, the capital per worker in urban industries is larger, which is the conventional definition of relatively high capital intensity. IMPACT OF GROWTH ON FID: QUALITATIVE ASPECTS 119

Table 3.10. Capital Intensity, by Region and Sector, 1961 and 1971

Fixed assets per employee (thousands of N.T. dollars) Ratio of Ratio of all Taiwan five largest Five Rural to rural cities to All largest prefect- prefect- rural Year and sector Taiwan citiesa uresb ures prefectures

1961 Manufacturing 48.35 45.13 49.97 0.97 0.90 Construction 37.64 58.65 19.93 1.89 2.95 Utilities 629.94 618.34 664.28 0.95 0.93 Trade 28.85 40.15 21.08 1.37 1.91 Services 61.91 98.00 26.30 2.95 4.67

1971 Manufacturing 96.09 124.57 63.71 1.51 1.96 Construction 32.43 52.99 11.45 2.83 4.62 Utilities 1,865.79 2,149.79 388.96 4.80 5.52 Trade 66.70 79.47 50.71 1.32 1.57 Services 127.27 180.57 43.43 2.93 4.58

Sources: ICCT, General Report, Industrial and Commercial Census of Taiwan, 1961 and 1971; figures for 1971 were compiled by Samuel Ho, Economic Develop- ment of Taiwan: 1860-1970 (New Haven: Yale University Press, 1978). a. The five cities are Taipei, Taichiung, Kaoshiung, Keelung, and Tainan. b. The rural prefectures are Miaoli, Taichiung, Changhwa, Nantou, Yunlin, Chiayi, Tainan, Kaoshiung, and Pengtung. every category of nonagricultural activity in both years, that the capital per employee was higher for urban areas (the five largest cities) than for all Taiwan and for rural areas. Moreover the two marginal exceptions, manufacturing and utilities in 1961, can be easily explained. First, sugar refining, which is large in scale, intensive in capital, and located in rural areas, played a substantial role in total manufacturing in 1961. If that and other such processing are excluded from manufacturing, the general pattern holds. Second, the capital intensity of utilities in 1961 was apparently affected by the installation of the country's largest power plant in rural Nantou Prefecture in that year. Finding 4.22 indicates that the Gini coefficient of wage income [G,] always received a heavier weight than that of property income [G,] (see figure 3.5). Moreover: FINDING3.12a. For urban industries and services, the time path of 120 GROWTH AND FID BY FACTOR COMPONENTS

0u/0' was mildly U-shaped-that is, it decreased before the turning point in 1968 and increased thereafter.

FINDING 3.12b. For rural industries and services, the time path of ./4r increased, except for one year. The explanation of these findings can be based on growth theory (see relations 3.1 and 3.2). Given the relative stability of real wages before 1968, relation 3.1 implies that small-scale rural industries and services responded more to the stimulation of low wages in the adoption of labor-using technology than did the large-scale urban industries and services, which tend to concentrate on a higher intensity of innovation (see the growing divergence in figure 3.5). Thus, contrary to the arguments of Lewis and others, labor's share [E.] can rise because of rapid increases in the total number of employees and the number of hours worked per employee, even during the phase when labor supply is unlimited and wages are more or less constant. This conclusion also implies that the more active promotion of labor-using technology could lead to a more favorable impact of growth on FID, even on urban FID, before the turning point. After the turning point, the ratio of the wage share to the property share [+w/,l generally increased in both sectors. According to relation 3.2, rapidly rising real wages accompanied by capital deepening caused that increase, which was somewhat more pronounced in the urban sector. In summary, the impact of the functional distribution effect on FIDcan be stated as follows:

FINDING 3.13a. Before the turning point the strong labor-using bias of technology change in rural industries contributed to FID equity for rural households, and the weak labor-using bias of technology change in urban industries made a modest contribution to FID equity for urban households.

FINDING 3.13b. After the turning point capital deepening and the labor-using bias both contributed to FID equity for all three models.

The factor Gini effect The factor Gini effect, defined in equations (3.16c) and (3.22d), captures the impact of changes in the factor Gini coefficients of wage, property, and agricultural income on the overall Gini coefficient [G,,]. What are the comparative magnitudes of the factor Gini IMPACT OF GROWTH ON FID: QUALITATIVE ASPECTS 121 coefficients in each of the three models? What are the longer term or trend characteristics of these Gini coefficients? What are the shorter term or transition characteristics of these Gini coefficients and their impact on G,? The findings related to these questions will be discussed first for wage and property income, then for agricultural income. In general: FINDING3.14a. Every Gini in the set (Ge,, Gu, GW)< any Gini in the set (GT, Gu,GT). FINDING 3.14b. In the set (G,, Gu, (Ur,),GU < G, and Gr < G,,,; in the set (GT, G', G'), Gu < G. and G" < GT.

FINDING 3.14c. G", < G: and G < G. The economic significance of finding 3.14a-that every wage Gini generally was less than every property Gini-is that it strengthens the intrasectoral conclusion of finding 3.1a. Not only was the inequality of wage income [G.] less than the inequality of property income [G,]; the inequality of rural wage income [G;1,] was less than that of rural property income [Gr ], and the inequality of urban wage income [Gu,] was less than that of urban property income [Gu]. Thus it again is evident, more concretely now, that the unequal distribution of property ownership contributed far more to FID inequality than its small distributive share might imply; wage income, which had by far the largest distributive share, contributed less to FID inequality than its share might imply. This conclusion can be further illustrated by figures 3.7, 3.8, and 3.9, which show the relative income shares of the highest 10 percent of the population to the lowest 10 percent. The results indicate that the ratio of property shares was about double the ratio of total incomes and treble the ratio of wage shares. The economic explanation of finding 3.14b-that sectoral Gini coefficients for wage and property income were less than total Gini coefficients for wage and property income-resides in the substantial gap in average wage and profit income between the rich and poor groups of a segmented population. A numerical example can illuminate this gap. Suppose in the extreme that the incomes of three low-income rural families and three high-income urban families are (Yr, Y-) = (1, 1, 1) (10, 10, 10). Then the Gini coefficients for both rural households and urban households are zero, but the Gini coefficient for all households is very large. Thus the inequality for 122 GROWTH AND FID BY FACTOR COMPONENTS

Figure 3.7. Ratio of the Total IncomneShare of the Top 10 Percent to That of the Bottom 10 Percent, by MlJodel,1964-72

Before turniing point After turning point

6 <-- -/,

-All households - - -Urban households 5 households -Rural

4 - I II I I I I I 1964 1966 1968 1970 1971 1972

Source: Calculated from DGBAS, Report on the Survey of Family Income and Expenditure, 1964-72.

all households necessarily is greater than the inequality for urban and rural households alone. This pattern is also illustrated in figures 3.8 and 3.9, where the ratios of relative income shares of property and wage income generally are less for urban households and rural households than for all households. The economic explanation of finding 3.14c-that rural Gini coefficients of wage and property income were less than urban Gini coefficients of wage and property income-is this: during most of the 1964-72 period, urban structural dualism, with its more substantial concentration of assets and wider variation in the scale of production, was more pronounced than its rural counterpart. More- over the degree of labor force heterogeneity, based on education, skill, age, and sex, was greater in urban areas than in rural areas. This pattern led to a more unequal distribution of wage income in urban areas than in rural areas. By 1972, however, the urban wage Gini fell below the rural wage Gini, implying two patterns demonstrated earlier in this section. First, rural dualism related to the gradual modernization of rural industry may have been catching up IMPACT OF GROWTH ON FID: QUALITATIVE ASPECTS 123

Figure 3.S. Ratio of the Wage Income Share of the Top 10 Peicent to That of the Bottom 10 Percent, by Model, 1964-72

8 _ Before turning point After turning point

5 _ Alll households - - -Urban householdzs ------Rural households 4

3 r 1964 1966 1968 1970 1971 1972

Source: Samieas for figure 3.7.

with urban dualism just when urban dualism was beginning to decline. Second, modernization may thus be said to have pene- trated the larger urban centers first and to a greater extent and to have permeated the smaller towns and, rural areas only later. The foregoing findings also provide an insight into the time patterns of the wage and property Gini coefficients of rural and urban households after the turning point (see figure 3.4):

FINDING 3.15a. The gap between the total wage Gini [G,] and the sectoral wage Ginis [Gw, and Gr] tended to narrow, as did the gap between the total property Gini [C-,,] and the sectoral property Ginis [G,uand Gr].

FINDI11G 3.15b. The gap between G' and GU tended to narrow, as did the gap between G, and Gu.

FINDING 3.15c. Thus (G,, Gu, Gr) tended to converge to a higher "limiting value" than (G., Gu, GW), which also were converging (see findings 3.14a, 3.15a, and 3.15b). 124 GROWTH AND FID BY FACTOR COMPONENTS

Figure 3.9. Ratio of the Property Income Share of the Top 10 Percent to That of the Bottom 10 Percent, by Model, 1964-72

Beforeturning point After turning point 20

\ All households _ ---- Urban households

1964 1966 1968 1970 1971 1972 S-urce: Sameas for figure 3.7.

The pattern of intersectoral gaps described in findings 3.15a and 3.15b reinforces the notion expressed in finding 3.14c that the difference in the economic forces affecting rural and urban industries tends to become less significant after the turning point, however pronounced that difference may have been eaxlier. That is, there is IMPAC1r OF GROWTH ON FID: QIUALITATIVE ASPECTS 125

Figure 3.10. Ratio of the Agricultural Income Share of the Top 10 Percent to That of the Bottomii10 Percent, by Mlodel, 1964-72

12 - Before turning point After turning point

- All households 10 ------RRural households

- I I I I I I I I - 1964 1966 1968 1970 1971 1972

Source:Same as for figure 3.7.

a tendency toward convergence as rural industrialization catches up with urban industrialization. Consequently these gaps are transi- tional characteristics encountered in the earlier stages of transition growth. Finding 3.15c nevertheless suggests that the gap between the property Gini and the wage Gini, identified in finding 3.14c, tends to persist after the turning point. This pattern suggests that such a gap is a permanent feature of any economy. FINDING3.16. There was a consistency between the patterns of wage and property Ginis both before and after 1968.

FINDING 3.16a. For rural households there was an overall U-shaped pattern: Ga, and G' slightly declined before 1968 and significantly increased thereafter. 126 GROWTH AND FID BY FACTOR COMPONENTS

FINDING 3.16b. For urban households there was an overall mildly inverse U-shaped pattern: Gu, and Gu stayed constant or slightly increased before 1968 and consistently declined thereafter. FINDING 3.16c. For all households there was an overall inverse U-shaped pattern: G,,, and G,, slightly rose before 1968 and consistently declined thereafter. This consistency of behavior of the Gini coefficients of wage income and property income for each model is, in the opinion of the authors, the result of intrasectoral structural dualism. That is, in both urban and rural industries, some large-scale units hiring higher quality labor and receiving higher rates of return coexist with smaller scale units hiring unskilled labor and receiving lower rates of return. The more pronounced this structural dualism is, the higher are the values for the Gini coefficients of wage income and property income. If the time pattern of these Gini coefficients is inverse U- shaped, as it is for urban industries and for the whole economy (findings 3.16b and 3.16c), an initial increase in structural dualism in both gives way to its gradual elimination after the turning point. Finding 3.16a implies that dualism in rural industries initially is less pronounced than, and only later catches up with, the dualism in urban industries. Findings 3.16a, 3.16b, and 3.16c facilitate the following summary statement about the impact of the nonagricultural factor Gini effect-that is, the factor Gini coefficient of wage and property income combined [G.j--on Gu,for the three models (also see tables 3.5, 3.6, and 3.7): lmpact of nonagricultural Gini on: Before 1968 After 1968 FINDING 3.17a. G, for all households Very Very unfavorable favorable FINDING 3.17b. Gy,for rural households Slightly Very favorable unfavorable FINDING 3.17c. Gv,for urban households Slightly Very favorable favorable Finally, in examining the agricultural Gini effect traced by the curve of the Gini coefficient of agricultural income [G.], it can be concluded that: SUJMMARYAND CONCLUSIONS 127

FINDING 3.18. The factor Gii effect caused by agricultural income was always favorable-that is, it was favorable for the rural-households and all-households models both before and after 1968 (see table 3.8). Thus the distribution of agricultural income among rural families was consistently becoming more equal over time and favorably contributing to overall FID.

Summary and Conclusions

In this chapter a technique for the decomposition of Gini coefficients was developed to enable forging causal links between growth and the distribution of income in a developing country. It was shown that distribution, as measured by the Gini coefficient [Gj, is very much affected by the particular forces of growth that a country experiences. In Taiwan, for example, the turning point signifying the exhaustion of surplus labor brought about a marked difference in the behavior of the Gini coefficient. In analyzing the causation of the change in G, and attempting to relate that change to growth, it helps to recognize that family income has a number of factor components which differ in type and in their impact on overall equity. The time path of G, affected by growth, can then be analyzed to determine the quantitative and qualitative impacts of three main effects: the reallocation effect, which captures changes in the share of agricultural income in total income; the functional distribution effect, which captures changes in the relative shares of property income and wage income; and the factor Gini effect, which captures changes in the inequality of factor income components. The quantitative and qualitative findings emerging from such analysis seem to support the notion that historical subphases of growth are relevant to the distribution of income as well. It is self-evident that governments of most LDcS, despite their limited fiscal capacity, can directly affect the distribution of income through taxes and transfers. But the main inference to be drawn from the findings here is that a change in the growth path is likely to be the most effective method of tackling the maldistribution of income. The experience of Taiwan-with unusually low levels of Gini coefficients,with an unusually mild Kuznets effect over time, and with no significant transfers through welfare payments-bears 128 GROWTH AND FID BY FACTOR COMPONENTS

out our conviction that significant and sustained changes in FID equity are mainly achievable through the modification of the basic forces underlying the pattern of growth-at least in the nonsocialist mixed economy. The findings for Taiwan also enable us to draw a number of more specific conclusions. For all households the findings demonstrate that the Kuznets effect, whatever trace of it remained, was caused mainly by the nonagricultural factor Gini effect-an effect which nevertheless can be substantially, if not totally, overcome by other forces. It is not surprising that reaching the turning point unambiguously benefits the overall distribution of income along with the objective of growth. What is surprising and important, the functional distribution of income, even before the turning point, does not necessarily make things worse, and the agricultural factor Gini effect substantially contributes to making things better. Early concentration on agricultural productivity thus provides additional income to rural families, encourages nonagricultural activity in rural areas, and increases the capacity of agriculture to equalize FID. At the same time, labor's share can rise because of increases in labor intensity, not because of rapidly rising wages. Under such conditions, the conflict between growth and the distribution of income can be eliminated, even before the turning point. For urban households equity probably cannot substantially improve until after the turning point, when the unfavorable impact of the functional distribution effect is reversed. The reason for this is that urban FID reflects the overall Kuznets pattern, but does not benefit from the ameliorating effects of agricultural income. The most dependable way to ensure consistency between growth and distribution for urban households is to advance the coming of the turning point by instituting vigorous programs for balanced growth and reallocation. Even before the turning point, much can be accomplished by selecting a relatively labor-intensive path for urban industry. For rural households the favorable trend of FID before the turning point is essentially derived from two sources. One is the beneficial contribution of the agricultural Gini coefficient, which shows a consistent and sustained pattern of decline. The other is the unusually dispersed pattern of the location of Taiwanese industry, a pattern which benefits the relatively poor rural families. As members of rural families, particularly poor rural families, shift to rural SUMMARY AND CONCLUSIONS 129 industries, the share of wage income rapidly rises and the share of agricultural income rapidly declines. Especially surprising is the finding of a rising wage share before the turning point for rural households and all households. It runs counter to the experience of most contemporary LDCS and to the arguments of Lewis, Kuznets, and Marxist and dependency theorists.34All these observers share one view: As growth really begins to get under way, distribution must worsen as the shares of rent and profit income rise. The presumed reasons are that the rich in both sectors accumulate more assets than the poor and that the shift from rural to urban activities increases the relative size of the sector demonstrating the more unequal distribution of income. This argument apparently neglects the possibility, demonstrated by Taiwan, that rent reductions in agriculture and a change in the relative position of workers can simultaneously occur and enable FID to be improved by the combination of a rising functional distribution of wage income and a falling agricultural income Gini overcoming all else. Consequently the Kuznets effect applies not at all to rural households in Taiwan and only slightly to urban households and all households. The analysis of this chapter clearly indicates the need to focus more attention on the wage share and the causes for its pattern of distribution. Although the reallocation effect and the functional distribution effect can be linked to certain familiar notions in growth theory, that level of formal analysis does not exist to guide attempts to explain the important factor Gini effect. Efforts to link the factor Gini effect more fully to growth, by examining the causes of the heterogeneity of human and physical capital, would thus seem to deserve a higher priority. Our effort to examine causes of the heterogeneity of human capital is described in chapter four.

34. See William R. Cline, "Distribution and Development," Jounal of De- velopment Economics, vol. 1 no. 4 (February 1975), pp. 359-400. CHAPTER 4

The Inequality of Family Wage Income

THREE INTERRELATED FORCES associated with economic development are the primary causes of the inequality of family wage income: the industrialization of economic activity, the differentiation of the labor force, and the alteration of rules governing family formation. The distribution of wage income, the largest component of national income and family income, is thus influenced by forces quite different from those influencing the distribution of property and transfer income. As capital is accumulated and technology becomes more advanced, the structure of industry rapidly changes. One aspect of this changing structure is the growing demand for a more diversified labor force. Industry not only becomes more sensitive to the distinction between skilled and unskilled labor; it demands a wider variety of workers having different attributes. At one end of the spectrum industry requires accountants, managers, lawyers, and doctors; at the other end, uneducated female workers. Consequently, when an LDC economy modernizes, the labor force is differentiated into various homogeneous groups which can be identified by the different combinations of labor attributes they embody. The attributes of sex, age, and education are the most prominent. The differentiation of the labor force thus is largely a response to changing industrial demand. That demand, coupled with the supply of labor in various homogeneous groups, determines the structure of wage rates at any given time. But the pricing of labor is both rational and irrational. Market forces operate to reward workers according to their productive contributions-that is, according to

130 THE INEQUALITY OF FAMILY WAGE INCOME 181 their respective marginal productivities. Concomitantly institutions discriminate against women and favor the members of wealthier families to reward workers of the same age and educational qualifications differently. Thus different wage rates prevail for different homogeneous groups of workers for both rational and irrational reasons. For societies in which the family is the basic labor-owning unit, the basic determinants of the structure of total family wage income are the size of the fanmilyand the labor attributes of its members. These determinants are in turn influenced by such factors as fertility patterns, family decisions to invest in education, and the transition from extended to nuclear families. Population growth, in addition to resulting in a larger and increasingly heterogeneous labor force, influences and is influenced by these same determinants. In the process of economic development, then, economic forces determine the wage rates of workers as individuals; demographic and sociological forces determine the grouping of these workers into families. The impact of economic development on demographic variables thus manifests itself in the patterns of family formation, patterns which naturally affect family wage income. To describe the heterogeneity of Taiwan's labor force, empirical data for 1966 is presented in this chapter.' That presentation includes descriptions of the wage structure, the classification of labor attributes, and the frequency distribution of workers according to that classification. The data are then analyzed at three levels. The first level investigates the extent to which the inequality of wage rates can be explained by various labor attributes. The second examines the causes of inequality of wage income for groups of individual wage earners. The third studies the causes of inequality of the distribution of wage income among families. Certain statistical techniques are used at each level of analysis. At the first level the statistical technique is the familiar linear regression method. At the

1. In the introduction a sharp distinction was drawn between published and unpublished DGBAs data. In this chapter use is made of the original unpublished data. For this reason the procedures adopted in the course of processing and coding the data from the original household survey are explained in detail in appendix 4.1 to this chapter. Only one year, 1966, has been singled out for intensive study: it is a high-quality early year; the emphasis here is essentially cross-sectional; and the requirements of manual coding and computerization are very substantial. 132 THE INEQUALITY OF FAMILY WAGE INCOME second and third levels the technique is based on decomposition equations for the model of additive factor components. But unlike the preceding chapter, which used linear approximations for purposes of decomposition, the general case of an exact decomposition is used here. Although these equations are mathematically derived in part two of this volume, their meaning and applicability are explained in this chapter for the benefit of the general reader who may not be rnathematically inclined.

Empirical Data

The labor force in a developing country typically is rather homogeneous before the transition to modern growth gets under way. During the transition the labor force tends to become more and more differentiated and heterogeneous. Although this heterogeneity has many facets, only the five most important characteristics, or variables, are examined here: sex, age, education, job location, and occupation. The sex variable has two values: female and male. The age variable has four values: under 25, 25-45, 45-60, and over 60. The education variable has five values: primary school or less, junior high school, senior high school, technical school, and university or more. The location variable has three values: rural, town, and city. The occupation variable has six values: public employee or serviceman, specialist or professional, service employee, commercial self-employee, manual laborer, and agricultural employee. When labor is classified according to the foregoing criteria, there result 720 types of labor or homogeneous groups. The purpose here is to analyze the impact of this heterogeneity of the labor force upon the degree of wage income inequality. Thus the data inputs required for this analysis consist of the wage rates and frequency distributions of the workers in each homogeneous group. Based on a sample survey of 2,777 workers for 1966, the average annual wage rate and the frequency distribution of workers are presented in tables 4.20-4.23 in an appendix to this chapter. In addition, these tables have been disaggregated to show separately the wage rates and frequency for rural workers in table 4.24, town workers in table 4.25, city workers in table 4.26, and all workers in table 4.27. The complexity and multidimensionality of issues associated with the inequality of wage income are evident even when only five labor characteristics are selected for analysis. Furthermore such a cross- EMPIRICAL DATA 133 listing of data, essential for applying the model of additive factor components, seldom is available in published form. And because the pattern of family ownership of the heterogeneous labor force underlies the inequality of family wage income, the family affiliation of workers is needed in addition. To provide a sense of the order of magnitudes associated with each labor characteristic, the sex, education, and age characteristics will be described for the whole economy by suppressing the location dimension. Relevant to all locations, these will be referred to as overall characteristics. The sex, education, and age characteristics will also be separately described for each location-that is, for rural areas, towns, and cities.

Overall characteristics Of the 2,777 workers covered in the 1966 survey, about 75 percent had completed only their primary education (table 4.1). Junior and senior high school graduates accounted for another 20 percent. With respect to sex, the completion of primary school significantly demarked the educational attributes of workers. Although the female percentage of graduates was higher than the male percentage for the lowest educational group, it was lower than the corresponding male percentage for all other educational groups. The figures reveal the expected pattern: fewer female workers than male workers received higher education. Because shortages of technical workers are generally regarded as a bottleneck for economic development, the low proportion, only 1.3 percent, of graduates of technical schools should also be noted. When the wage rate of each educational group is expressed as a multiple of that of the primary school group, it is seen that junior high school and university were the most important steps for up- grading the earning power of workers. Three years of junior high school brought about a more than doubling of the wage rate; three additional years of senior high school brought about practically no further improvement. The wage index for junior high school was 2.2 (primary school = 1); that for senior high school was 2.32. Another two years of technical school led to an improvement in the wage index to 2.95. But university education brought about a really significant improvement to 4.18. It seems that solid economic reasoning justified both the strong pressure on high school graduates to pass the college entrance examination and the popular feeling that those who did not enter college were failures. 134 THE INEQUALITY OF FAMILY WAGE INCOME

Table 4.1. Relative Wage Rates and Frequency Distribution of Labor, by Education, Sex, and Job Location, 1966 (percent)

Junior Senior Techni- Univer- Primary high high cal sity or Item school school school school over Total

All workers Percentage distribution 73.93 8.46 12.45 1.33 3.83 100.00 Female 82.59 7.10 8.50 0.97 0.84 100.00 Male 70.90 8.94 13.84 1.46 4.86 100.00 Relative wage rate (primary school = 1.00) 1.00 2.22 2.32 2.95 4.18 1.85

Rural workers Percentage distribution 89.20 4.65 5.15 0.50 0.50 100.00 Relative wage rate (rural areas = 1.00) 1.00 1.00 1.00 1.00 1.00 1.00

Town workers Percentage distribution 70.40 9.81 14.80 1.06 3.93 100.00 Relative wage rate (rural areas = 1.00) 1.54 1.01 1.08 0.91 1.21 1.71

City workers Percentage distribution 63.59 10.29 16.36 2.64 7.12 100.00 Relative wage rate (rural areas = 1.00) 2.64 2.74 1.39 0.97 1.80 2.98

Sources:Tables 4.20-4.27appended to this chapter.

More than half the workers were in the 25-45 age group (table 4.2). The under-25 age group accounted for a quarter of workers; the rest were mainly allocated to the 45-60 age group. When the corresponding percentages of female and male workers are compared, the contrast between the lowest group-that is, the under-25 group-and the other groups once again shows the significance of the influence of the sex characteristic. Although the percentage of female workers was much higher than the percentage of males in the youngest group, it was lower than that for males in all the other age groups. As would be expected, female workers retire from the labor force at a much earlier age than their male counterparts because of their role in the family. EMPIRICAL DATA 135

Table 4.2. Relative Wage Rates and Frequency Distribution of Labor, by Age, Sex, and Job Location, 1966

Under Over 25 25-45 45-60 60 Item years years years tyears Total

All workers Percentage distribution 24.70 53.84 19.30 2.16 100.00 Female 44.71 44.71 9.75 0.84 100.00 Male 17.73 57.02 22.63 2.62 100.00 Relative wage rate (under 25 = 1.00) 1.00 2.24 2.79 2.13 2.04

Rural workers Percentage distribution 28.14 55.15 15.20 1.51 100.00 Relative wage rate (rural areas = 1.00) 1.00 1.00 1.00 1.00 1.00

Town workers Percentage distribution 22.32 55.10 18.48 2.45 100.00 Relative wage rate (rural areas = 1.00) 1.36 1.68 2.03 1.06 1.71

City workers Percentage distribution 24.93 50.40 22.30 2.37 100.00 Relative wage rate (rural areas = 1.00) 1.79 3.14 3.11 3.10 2.98

Sources: Tables 4.20-4.27 appended to this chapter.

When the wage rate of each age group is expressed as a multiple of that of the youngest group, it is seen that the gain in the wage rate was most significant for those in the 25-45 age group and much less significant for the 45-60 age group. The wage index for the 25-45 age group was 2.24 (under 25 = 1); that for the 45-60 age group was 2.79; that for the over-60 age group was 2.13. The reward for experience therefore manifested a strong trend toward diminishing return. The probable reasons for this are that "age" is a poor proxy for experience and that the advantage of experience gained with 136 THE INEQUALITY OF FAMILY WAGE INCOME

Table 4.3. Wage Parity of Female Workers, by Age and Education, 1966 (male wage rate = 1) Level of education Under 25 25-45 45-60 Over60 Total

Primary school 0.7099 0.4077 0.3779 0.4937 0.4235 Junior high school 0.7903 0.5272 0.5307 - 0.4638 Senior high school 0.9304 0.7958 1.0115 - 0.7215 Technical school 1.4468 0.7533 - - 0.7253 University or over 1.0292 0.6372 0.5651 - 0.5798

All levels 0.7688 0.4244 0.4228 0.2984 0.4170

- Not applicable. Soutrce: 'Table 4.27 appended to this chapter. higher age is offset by other disadvantages of "aging" for workers over 60. The foregoing data reveal that female workers were heavily allocated to age and educational groups that received low pay. The concentration of females in low-paying jobs may have been the result of their free choice to join and to leave the labor force early. There may also have been institutional discrimination in the availability of jobs for female workers. Wage discrimination is less disputable (table 4.3). For all groups the wage rate for females was substantially less than half that for males. Female workers were at a disadvantage in every educational group. -Moreover discrimination was higher for the low educational categories, which absorbed almost 90 percent of female workers. The wage rate for females having primary education was 42 percent of that of their male counterparts; that for females having junior high school education, 46 percent. Discrimination against female workers also prevailed for every age group, and the severity of discrimination increased with age. Consequently, elderly women with little education were apt to be most disadvantaged; young women with higher education, least disadvantaged.

Locational characteristics The concentration of less educated workers in the rural sector was high (see table 4.1). Primary school education significantly demarked the job-location characteristic. The proportion of this EMPIRICAL DATA 137 group was highest in the rural areas and lowest in cities-89.2 percent compared with 63.6 percent. For all other educational categories the opposite was true: the proportion of high-education graduates was greatest for the cities and lowest for the rural areas. In educational attainment, labor in a tradition-bound rural economy is an inferior homogeneous group. With the rural areas, towns, and cities respectively characterized by increasing degrees of modernization and urbanization, modernization brought about labor heterogeneity in a particular sense: the formation of a superior homogeneous educational group. Although this conclusion is based upon a cross-sectional study, it can and should be verified by the analysis of time series in the future. When the wage rate of each locational group is expressed as a multiple of the rural wage rate for each educational group, the most significant gaps prevail between city workers on the one hand and town and rural workers on the other. For the two lowest educational groups, the wage rate for city workers was almost three times that of rural workers. For higher educational groups, the wage disparities were less. For the technical school groups, city workers had practically no advantage. Turning to the age characteristic, it can be seen that the rural sector provided more employment opportunities for younger workers than cities did. The proportions of rural workers in the under-25 and 25-45 age groups respectively were 28.1 percent and 55.2 percent; those of urban workers, 24.9 percent and 50.4 percent. For workers over 45 the town and city offered increasingly greater opportunities. Modernization therefore seems to lengthen the working life. Because older workers had a higher earning power than their younger counterparts, modernization appears to lead to the formation of a superior wage-earning group much in the manner that education does (see table 4.2). For all age groups, workers in towns and cities received higher wage rates than rural workers. But this disparity was not as great for young workers as it was for all other age groups. For those in the under-25 age group, the wage indexes of town and city workers respectively were 1.36 and 1.79 (rural workers = 1). The reason for this pattern may be that young rural workers were more willing than old workers to migrate to large cities, a propensity that would result in a smaller wage gap in the youngest age group. Job location thus represents a significant dimension for the analysis of inequality in the distribution of wage income. For this reason 138 THE INEQUALITY OF FAMILY WAGE INCOME the three locations are separately treated in the remainder of this chapter.

Analytical Framework

The analysis of the inequality of wage income thus comprises three distinct types, or levels, of problems: at the first level the problem is to determine the impact of labor heterogeneity on the wage rate; at the second, the causes of the inequality of wage income among homogeneous groups of individual workers; at the third, the causes of the inequality of family wage income. It should be perfectly clear that the focus of this chapter, indeed this entire volume, is the inequality of family wage income. Although the first two levels of analysis may be of interest in their own right, they are discussed in this chapter primarily to lay the foundation and constitute the input for the third level of analysis. The association of various dimensions of labor heterogeneity with the magnitude of the wage rate perhaps is one of the most popular methods for studying the inequality of wage income. For example, the familiar earnings-function approach uses a linear regression model in which the wage rate is regressed on various labor force characteristics; which are represented by natural and dummy variables.2 The purpose of this technique is to estimate regression coefficients that can be interpreted as quantified causes of the inequality of the wage rate. The regression coefficientsof the wage rate on such characteristics as age, sex, and educational attainment represent the premiums associated with these characteristics-that is, the extra wage income additively accruing to workers having different combinations of values for these characteristics. This earnings-function technique has nothing to do with the inequality of wage income in the sense used in this volume. Inequality here refers to the degree of inequality of income for a group of income recipients [W = (WI, W2, . . . , W,)] as measured by the Gini

2. See Jacob Mincer, Schooling, Experience, and Earnings (New York: Na- tional Bureau of Economic Research, distributed by Columbia University Press, 1974) and Sherwin Rosen, "Human Capital: A Survey of Empirical Research," in Research in Labor Economics, ed. Ronald G. Ehrenberg (Greenwich, Ct.: JAI Press, 1977), vol. 1, pp. 3-39. ANALYTICAL FRAMEWORK 13.9 coefficient [Gm]. The earnings-function technique is concerned neither with the pattern of wage income [W]j nor with its degree of inequality [Gm]. Nevertheless the earnings function used at the first level of analysis provides certain research inputs required at the second and third levels. With this technique such demographic characteristics of labor as sex, age, and educational attainment can be additively associated with such economic magnitudes as wage income. Given the basic purpose of this chapter, which is primarily directed at the analysis of wage income inequality for homogeneous groups of individual workers and for families, only a rather naive version of such an earnings function is used here. It can clearly be improved as an input to this work. Methodologically, however, it should be obvious that the primary interest here is with the way an earnings- function technique can be combined with the additive factor-components technique, not with the perfectibility of the earnings function itself. The analytical design used in combining these two techniques is discussed more fully in an appendix to this chapter. At the second level of analysis workers are treated as individuals and all information on their family affiliation is still suppressed. Given the pattern of wage income of individual workers [W = (W1, WT2, . . , W.)] and the degree of wage income inequality EGQg,the crucial analytical task at the second level is to determine the extent to which each of the labor characteristics accounts for Gw. At the first level of analysis the wage-rate inequality attributable, for example, to the sex characteristic is traced to such rational forces as differences in worker productivity and to such irrational forces as sex discrimination. The second level of analysis addresses the same set of socioeconomic forces, but attempts to assess their impact on the degree of inequality of wage income [Gm], not on the wage rate. This analysis will be formulated as an additive factor-components problem and make use of the earnings-function results from the first level of analysis. Analysis of the inequality of family wage income at the third level requires information on the family affiliation of workers. The technique for this analysis can be illustrated with a simple model examining two labor characteristics, sex and education (table 4.4). The data in this table correspond to the cross-listing of information on the wage rate and frequency distribution of workers in appendix tables 4.20-4.23; they also provide all the information needed for analysis at the second level. For analysis at the third level, the ten workers in table 4.4 are classified into five families to show total 140 THE INEQUALITY OF FAMILY WAGE INCOME

Table 4.4. Numerical Example Corresponding to the Cross-listing of Information on the Wage Rate and FrequencyDistribution of Workers in Tables 4.20-4.27, by Sex and Level of Education

Inter- Low mediate High Item education education education

Wage Rate Female workers 2 5 10 MA'aleworkers 3 7 15 Number of Workers Female 1 4 1 Male 2 1 1

Note: W = (2, 3, 3, 5, 5, 5, 5, 7, 10, 15) Source: Constructed by the authors.

family wage income [Y] and to trace the wage income components to the membership composition of families (table 4.5). The six grades of labor in this table correspond to those in table 4.4. The pattern of total family wage income [Y = (5, 8, 10, 15, 22) ] results in a Gini coefficient [GJ] of 0.2733. This illustrative numerical example indicates the way the analysis of G,, will be formulated as an additive factor-components problem at the third level. The total family wage income obviously depends on family size- that is, on the number of wage earners owned by the family-as well as membership structure. A column in table 4.5 describes the pattern by which workers of a particular grade are distributed among the families. It is apparent that the unevenness of this distribution can be a major cause of the inequality of family wage income. A family with high wage income would be expected to "own" more high-grade workers, such as college-educated males, than would a family with low wage income. In addition, the membership composition of families, described by the sex, age, and educational attainment of their members, is determined by the rules of family formation. These rules are affected by a host of sociodemographic factors, including the institution of marriage, the patterns of reproduction, and the properties of nuclear families in transition. Thus the third level of analysis encounters wholly new factors which are LABOR HETEROGENEITY AND THE WAGE RATE 141

Table 4.5. Numerical Example Classifying Workers into Five Families and Tracing Wage Income Components to the Membership Composition of Those Families

Low Intermediate High education education education Total wage Fe- Fe- Fe- Family income male Male male Male male Male

Familv 1 5 0 0 5 0 0 0 Family 2 8 2 6 0 0 0 0 Family 3 10 0 0 0 0 10 0 Family 4 15 0 0 15 0 0 0 Family 5 22 0 0 0 7 0 15

Note:The pattern of family wageincome is given by Y = (5, 8, 10, 15, 22), and the resulting Gini coefficientis 0.2733. Source:Constructed by the authors with data from the numericalexample of table 4.4.

not encountered at the first two levels of analysis and which are traditionally treated by such other disciplines as sociology and demography. Because this area of inquiry is relatively new for economists, we will be content to speculate about the way the problem can be formulated in future research efforts.

Labor Heterogeneity and the Wage Rate: First-level Analysis

Multiple regression analysis is used to analyze the impact of labor heterogeneity on the wage rate. Let W be the wage rate, and let

XI, X2, . . ., XI be the explanatory variables. A regression equation can then be specified as follows:

(4.1) W = a + aix + a2X2 +... + arxr + where a is a random error term. The r explanatory variables [xei] represent the various characteristics that define the heterogeneity of the labor force. The purpose of the regression analysis is to estimate the coefficients [ai] that measure the quantitative impact of 142 THE INEQUALITY OF FAMILY WAGE INCOME each labor dimension upon the wage rate under the assumption of independence. In applying the regression analysis to the data for 1966 (see appendix tables 4.20}4.23), the regression equation is specified as:

(4.2) W = a. + aix, + a2X2 + a3x3 + a4X4 + 5.

In addition to the variables representing sex [xi], education EX2], and age [EX], an additional variable [X4 ] represents the total income of the family to which a given wage earner belongs.8 The reason for using such a variable is to determine whether a wealthy family can exercise undue influence to secure a higher wage rate for its members. Equation (4.2) will be applied separately to each of three job locations: rural areas, towns, and cities. The explanatory variables [xi] can be assigned a range of values. The sex variable [Ex] takes on the value of zero for females and 1 for males; the coefficient a1 thus measures the male premium. The education variable [x2] takes on values that correspond to the years of formal education completed (6, 9, 12, 14, or 16). The coefficient a2 thus measures the education premium and corresponds to the market value of one additional year of formal education. The age variable [Ex] takes on values that correspond to an ordinal ranking of age as a proxy for the contribution of experience to wage- earning power (1, 2, 3, or 3).4 The coefficient a3 thus measures the age premium and corresponds to the value of experience in earning power. Total family income [Z4] is measured in thousands of new Taiwan dollars.5 The coefficient a4 thus measures the nepotism premium associated with undue family influence on the earning power of its members. This model was applied to the primary data in appendix tables 4.20-4.23. It is apparent from the sample sizes that the regression coefficients are very significant (table 4.6). In cities, where the average wage rate in 1966 was NT$19,831, the male premium was

3. See schedule 4.5 in appendix 4.1 to this chapter for the coded form used to assemble data on total family income. 4. Noticethat the over-60age group is assigneda rank of 3, or the same as that assigned to the 45-60 age group. This choice was made after experimentation with several alternative rankings for the four age groups: (1, 2, 3, 1.5), (1, 2, 3, 2), (1, 2, 3, 2.5), and (1, 2, 3, 3). The last ranking was selected because it leads to the highest value of the coefficient of determination (R2 = 0.5). 5. At the time of writing, the new Taiwan dollar was equal to about US$0.025. LABOR HETEROGENEITY AND THE WAGE RATE 143

Table 4.6. Regression Coefficients of Four Explanatory Variables, by Job Location, 1966

Regressioncoefficient

Nota- Item tion Rural area Town City

Constant a. -10.8977 -12.1360 -18.8349 (-12.2398) (-12.2728) (12.2333) Sex al 3.3770 5.2287 7.3493 (8.4366) (9.0333) (7.3777)

Education a2 1.4522 1.5537 1.5089 (12.9158) (17.7580) (11.3366) Age a3 1.7635 2.8801 6.2734 (6.2578) (7.6676) (10.4305) Total family income a4 0.0841 0.0800 0.1757 (7.1972) (6.9843) (9.3398)

Sample size 796 1,223 758

Note: Values in parentheses are t scores. The following values have been assigned to characteristics: Xi = (female, male) = (0, 1) X2 = (primary school, junior high school, senior high school, technical school, university) = (6, 9, 12, 14, 16) X3 = (under 25, 25-45, 45-60, over 60) = (1, 2, 3, 3) X4 = (total family income in thousands of N.T. dollars) Source: Calculated from tables 4.20-4.27 appended to this chapter.

NT$7,349, the age premium was NT$6,273, and the education premium was NT$1,509. For earning power, one year of formal education was therefore equivalent to about four to five years of informal education or experience, as measured by a simple gain in age. Being female was equivalent to the disadvantage of having almost five years less formal education. The locational specifications of rural area, town, and city represent an increasing degree of penetration by the forces of modernization into socioeconomic life. It appears, moreover, that the attributes of labor were probably evaluated (priced) with more sensitivity 144 THE INEQUALITY OF FAMILY WAGE INCOME

Table 4.7. Influence of Total Family Income on Wage Rates, by Sex and Age, 1966 (thousands of N.T. dollars)

Female Male

25-45 45-60 25-45 45-60 Item years years years years

Without family income effect- Senior high school 11.8187 18.0921 19.1680 25.4414 Technical school 14.8365 21.1099 22.1858 28.4592 University or over 17.8543 24.1277 25.2063 31.4770 With family incomeeffect Senior high school 13.5757 19.8491 20.9250 27.1984 (29.3887) (35.6621) (36.7380) (43.0114) Technical school 16.5935 22.8669 23.9428 30.2162 (32.4065) (38.6799) (39.7558) (46.1292) University or over 19.6113 25.8847 26.9606 33.2340 (35.4243) (41.6977) (42.7736) (49.0470) Ratio of the wagerate influencedby high family income to that influenced by low family incomeb Senior high school 2.1611 1.7967 1.7557 1.5814 Technical school 1.9530 1.6915 1.6604 1.5233 University or over 1.8063 1.6109 1.5865 1.4758

Note: Values in parentheses are t scores. Higher education is taken to be a proxy for higher wage income. Source: Calculated from tables 4.20-4.27 appended to this chapter. a. Computed from equation (4.2) by setting the variable for total family income equal to zero. b. Values for total family income of NT$100,000 and NT$10,000 were substituted into equation (4.2) to examine the effects of family income on the wage rate. in the commercialized milieu of large cities than in the traditional rural communities. The male premium of 7.35 in cities was more than double that of 3.38 in rural areas. Either male workers in cities had a higher productive power or, more likely, the discrimination against women was greater. For the age characteristic the difference between cities and rural areas was even greater. The age LABOR HETEROGENEITY AND THE WAGE RATE 145

Table 4.8. Distribution of Families, by Job Location and Total Family Income, 1966

Number of families Totalfamily income Rural (N.T. dollars) area Town City

Less than 10,000 28 46 7 10,000-15,000 70 94 28 15,000-20,000 85 133 46 20,000-25,000 68 114 65 25,000-30,000 48 94 64 30,000-40,000 52 104 87 40,000-50,000 30 51 59 50,000-60,000 8 35 29 60,000-70,000 13 16 23 70,000-80,000 6 11 6 80,000-100,000 7 8 10 More than 100,000 2 6 8

Source:Tables 4.20-4.27appended to this chapter. premium of 6.27 in cities was more than triple that of 1.76 in rural areas. For the education characteristic the difference between cities and rural areas was not significant. It would appear that rural areas are less sensitive than cities in their pricing of age and sex attributes of workers, but equally sensitive in pricing educational attributes. In a society in which families have a long tradition of playing a prominent social role, family influence would be expected to be significant in securing better paid positions for its members. The nepotism coefficient [a 4] measures the extent of the influence of total family income on the wage rates of family members. The nepotism premium of 0.18 in cities was more than double that of 0.08 in towns and rural areas. A better view of the quantitative significance of nepotism in cities can be provided by examining higher wage-income groups, proxied by educational attainment, for which family influence would be expected to be strong (table 4.7). The values in the first part of this table do not take into account the influence of family income; they were computed from equation (4.2) by setting the variable for total family income [Z4] 146 THE INEQUALITY OF FAMILY WAGE INCOME equal to zero. The values in the second part of this table do take into account the influence of family income. Because the vast majority of city families receive total income ranging from NT$10,000 to NT$100,000 (table 4.8), these two values were substituted into equation (4.2) to examine the effects of family income on the wage rate. The ratios of the wage rate influenced by high family income to the wage rates influenced by low family income are given in the third part of table 4.7. It can be seen that the wage rates a very wealthy family can secure for its members are at least 50 percent higher than those a very poor family can secure for its members. Given the value of the regression coefficienta 4 of 0.1757, the nepotism premium was worth approximately NT$1,800 a year, or NT$150 a month, for every increase of NT$10,000 in total family income.

Inequality of Income of Individual Wage Earners: Second-level Analysis

The regression analysis revealed the impact of various dimensions of labor quality on the wage rate. This section investigates causes of the degree of inequality of wage income for a group of individual wage earners. The method of analysis is based on the application of the following decomposition equation to the data for 1966:

(4.3) G. = 4qR1G1 + 02R 2G2 + . . . + 40/,RrGr+ A. In this equation the Gini coefficientof the wage rate [EG],or the wage Gini, measures the degree of inequality of wage income. Notice when the wage rate is calculated on an annual basis that the wage rate is the same as wage income. The r terms on the right side represent the various dimensions of labor quality. In this analysis r is equal to 4. The four terms stand for sex, education, age, and total family income and correspond to the four variables of regression equation (4.2). The aim of the decomposition analysis is to assess the quantitative impact, or contribution, of the various labor characteristics on G,. The term A will be referred to as the rank-weighted error term. Every term OiRiGiin equation (4.3) is the product of three factors. The factor Gi measures the degree of inequality of a particular attribute or characteristic and will be called the labor characteristic Gini. The factor 4i measures the share of inequality contributed by INEQUALITY OF INCOME OF INDIVIDUAL WAGE EARNERS 147 a characteristic and will be called the labor characteristic weight. The factor Ri measures the correlation between the values of labor characteristics and wage income and will be called the labor correlation characteristic. Before the empirical analysis, each factor will be precisely defined and given an economic interpretation with the aid of a numerical example.6

Labor characteristic Gini Suppose that five wage earners have wage income [we] as shown in the numerical example of table 4.9. The sex, educational attainment, and wage income of these workers constitute the primary 7 data in this numerical example. The sex variable [X1] takes on the value of zero for females and 1 for males. The education variable [EX] takes on the value of 1 for low education, 2 for intermediary education, and 3 for high education (the terms low, intermediary, and high conform to usage in Taiwan). Wage income is measured in thousands of new Taiwan dollars. When there are n families, this data can be summarized by vector notation:

(4.4a) W = col(w1, W 2, ... , Wn) and [wage pattern]

(4.4b) Xi = col(xil, i2 . . xZi.)- (i =- 1, 2, . . ., r) [labor characteristic pattern]

For any nonnegative column vector [Y = col( Yl, Y2, ... , Yn)] the Gini coefficient [Gd] can then be computed from the following equation': (4.5a) 0

(4.5b) GD,= aU, - ;

(4.5c) a = 2/n; ,B = (n + 1)/n;

6. See equation (12.13) and the accompanying discussion in chapter twelve of part two. 7. It is evident that the columns for primary data on sex and education in table 4.9 provide all the information for the frequency distribution that is essential for analysis at the second level (see table 4.5). 8. See chapter eight in part two for a fuller exposition. 148 THE INEQUALITY OF FAMILY WAGE INCOME

Table 4.9. Numerical Example of Regression Analysis for Five Wage Earners and Two Explanatory Variables

Primary data

Wage income Sex Education

Item [WI [Zx]a [X21a

Wage earner 1 w, = 2.01 X:I = 0 X21 = 1

Wage earner 2 W 2 = 4.98 X12 = 0 X22 = 2 Wage earner 3 W 3 = 7.01 Z13 = 1 X23 = 2 Wage earner 4 W4 = 7.97 X1 4 = 0 X24 = 3 Wage earner 5 ws = 10.03 X15 = 1 X25 = 3 Vector notation W XI X2 Mean value J = 6.04 X1 = 0.4 2= 2.2 Labor characteristic weight - - - Labor characteristic Gini - G,= 0.6000 G2 = 0.1818

Correlation characteristic b,c - R,= 0.666 R2 = 1.000

Rank-weighted error term d -

Wage Gini e G, = 0.2379

- Not applicable. Source: Constructed by the authors. a. See the text for the assignment of values to these variables. b. Ri = G1/G 1, where GI = 2/5 (1 X 0 + 2 X 0 + 3 X - + 4 X 1) - 6/5 = 0.2 c. R2 = G2/G2, where G2 = 2/5(1 X 1/11 + 2 X 2/11 + 3 X 3/11 + 4 X 4/11 + 5 X 5/11) d. A = [1/15 X (0.01) + 2/15 X (-0.02) + 3/15 X (0.01) + 4/15 X (0.03) + 5/15 X (0.03) ]/6.4 = 0.004688 e. G.= 4iRiG + - 2R2G2 = 0.125 X 0.666 X 0.600 + 1.03125 X 1 X 0.1818 + 0.04688 0.2379

(4.5d) u, = Xlyl + X2y2± ... + X.y.;

(4.5e) Xl = 1, X2 = 2. X. = n;

(4.5f) yi = YU/S,; (i = 1, 2, ... , n)

( 4 .5g) S = YI + Y2 + ... + Yn. INEQUALITY OF INCOME OF INDIVIDUAL WAGE EARNERS 149

Regressionanalysis Regressioncoefficient Estimated wage Regression a, =-1 a, = 2 a2 = 3 income error la.1 [aixl] [a2x2] [W1 [Sc]

-1 0 3 w, = 2 al = 0.01 -1 0 6 w2 = 5 a2 =-0.02 -1 2 6 W'3 = 7 a3 = 0.01 -1 0 9 W4 = 8 a4 =-0.03 -1 2 9 w54= 10 85= 0.03

a. a,x, a2X2 Wac a 0 =-1 altj = 0.8 a2,2 = 6.6 W= 6.4 &=0

- 61= 0.125 02 = 1.03125 _ _

0.004688

Expression (4.5a) emphasizes that all values of Yi must be rearranged in a monotonically nondecreasing order to compute G. Then Xi is the rank of Yi, and yi is the fraction of YT in total income EY]. When this formula is applied to the wage pattern EW] in equation (4.4a), the wage Gini [Gm] is obtained to measure the degree of inequality of the wage pattern [W]. When the same formula is applied to the labor characteristic patterns [Xi] in equation (4.4b), the various labor characteristic Ginis EGi] are obtained. In the numerical example the wage Gini [CG] is 0.24, the sex Gini [CG] is 0.60, and the education Gini [G2 ] is 0.18. The notion of the labor characteristic Gini [Gi] is meaningful only when the values of a characteristic variable indicate wage- earning power, at least in the ordinal sense. To illustrate: The values of the sex variable [xi] of zero for females and 1 for males presume that a male worker has higher earning power than a female worker. 150 THE INEQUALITY OF FAMILY WAGE INCOME

If all workers are male, the sex Gini [Ga] is zero. Extreme equality means that the group of workers is completely homogeneous with respect to sex. If all workers have completed only primary education, the education Gini [G2] would also be zero, indicating that the group of workers is homogeneous with respect to education. In these extreme cases, sex and education obviously cannot cause wage income inequality because the terms sbRiGl and 402R2G2 would both be equal to zero in equation (4.3). What is the common-sense meaning of the value of the labor characteristic Gini [EG]? Consider a numerical example with eight workers, where 1 stands for primary education or less and 2 stands for secondary education. The education structures of the eight workers are given by the row vectors of the labor characteristic patterns in the top part of table 4.10. Starting with the homogeneous group of uneducated workers in a traditional economy, the group of workers is slowly transformed into a homogeneous group of educated workers in a modernizing economy. During this transformation the education Gini first increases to a maximum value of 0.1705 and then decreases as the fraction of poorly educated or inferior workers declines, resulting in an inverse U-shaped pattern. Now consider a numerical example, again with eight workers, where 1 stands for primary education or less and 3 stands for university education or more. The education structures are given by the row vectors in the bottom part of table 4.10. During the transformation of the homogeneous group of uneducated workers to the homogeneous group of university-educated workers, the inverse U-shaped pattern is again produced. But with a maximum value for GL of 0.2679, the amplitude of fluctuation is much greater.9 The same numerical example can be used, in reverse, to illustrate the formation of a new inferior group. Suppose that 1 represents female and 2 represents male and read upward from the last row of the first part of table 4.10. Starting with the all-male labor force of a traditional economy, female participation gradually increases. Thus an inverse U-shaped pattern of the labor characteristic Gini is observable over time, whether the splinter group formed is super-

9. This inverse U-shaped pattern is independent of the index of inequality chosen. The same pattern is seen when the standard deviation or mean deviation is used as the index of inequality (see the last two columns of table 4.10). INEQUALITY OF INCOME OF INDIVIDUAL WAGE EARNERS 151

Table 4.10. Numerical Example of the Formation of New Homogeneous Groups with Eight Workers

Fraction in Labor characteristic inferior Gini Standard Mean patterna group coefficient deviation deviation

(1,1,1,1,1,1,1,1) 1.000 0.0000 0.0000 0.0000 (1,1,1,1,1,1,1,2) 0.875 0.0972 0.3308 0.2188 (1,1,1,1,1,1,2,2) 0.750 0.1500 0.4330 0.3750 (1,1,1,1,1,2,2,2) 0.625 0.1705 0.4841 0.4688 (1,1,1,1,2,2,2,2) 0.500 0.1677 0.5000 0.5000 (1,1,1,2,2,2,2,2) 0.375 0.1442 0.4841 0.4688 (1,1,2,2,2,2,2,2) 0.250 0.1071 0.4330 0.3750 (1,2,2,2,2,2,2,2) 0.125 0.0583 0.3308 0.2188 (2,2,2,2,2,2,2,2) 0.000 0.0000 0.0000 0.0000

(1,1,1,1,1,1,1,1) 1.000 0.0000 0.0000 0.0000 (1,1,1,1,1,1,1,3) 0.875 0.1750 0.6614 0.4375 (1,1,1,1,1,1,3,3) 0.750 0.2500 0.8660 0.7500 (1,1,1,1,1,3,3,3) 0.625 0.2679 0.9682 0.9375 (1,1,1,1,3,3,3,3) 0.500 0.2500 1.0000 1.0000 (1,1,1,3,3,3,3,3) 0.375 0.2083 0.9682 0.9375 (1,1,3,3,3,3,3,3) 0.250 0.1500 0.8660 0.7500 (1,3,3,3,3,3,3,3) 0.125 0.0795 0.6614 0.4375 (3,3,3,3,3,3,3,3) 0.000 0.0000 0.0000 0.0000

Source: Constructed by the authors. a. 1 = primary education or less; 2 = secondary education; 3 = university education or more.

ior or inferior. This is reminiscent of the Kuznets hypothesis that income distribution will worsen before it gets better. The foregoing ideas can be formulated more rigorously. Suppose that a given labor characteristic has two values, V1 and V2, and

that V, is less than V2. The value for the privileged group is V 2 ; that for the less privileged group is V1. Suppose further that there are n, workers in the less privileged group and n2 workers in the privileged group. The Gini coefficient of this labor characteristic 152 THE INEQUALITY OF FAMILY WAGE INCOME for all workers (n1 plus n2) isl":

(4.6a) G = n1n2 (V 2 - VI) or (niVI + n2V2) (n, + ni)

(4.6b) G = 0102 s where

(4.6c) 0, = ni/(n 1 + n2), 02 = n 2/(n, + n2),

V* = V1 /(V 1 + V2), V2* = V2/ (Vl + V2); (4.6d) s = V2*-VI with O < s < 1;

(4.6e) 01+ 02 =1; and

(4.6f) VI + V2* = 1. The term 01is the fraction of labor in the first group, and VI*is the relative value of the characteristic for that group. The term 02 is the fraction of labor in the second group, and V2*is the relative value of the characteristic for that group. The term s is the gap between Vi* and V2*. Using equations (4.6e) and (4.6f), rewrite equation (4.6b) as:

(4.6g) G = -2s0 -- 1 + s - 2s01 This equation makes G a function of s and 01. To determine the impact of the variation of 01 on G, partially differentiate equation (4.6g) with respect to 01:

aG (l + s - 2s0 -)-(1-201 - (01- _02) (-2s) (4.7a _ (4.7a) 00l (1 + s - 2s0I) 2/2s Thus: aG (4.7b) = 0 if and only if (01 - al) (02- a2) = 0, where

2 (4.7c) a1 = (1 + s - /l - s )/2s,

(4.7d) a2 = (1 + S + -I - s2)/2s, and

(4.7e) 0 < al < 1 < a 2.

10. See theorem 8.2 in chapter eight of part two. INEQUALITY OF INCOME OF INDIVIDUAL WAGE EARNERS 153

Figure 4.1. The Emergence of Splinter Groups

1.C A

S=1.0

0.8 0. = - 1

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Fraction of labor [O]

Source: Constructed by the authors.

Hence:

(4.7f) aG/e 1 > O for O < Ol < a, and (4.7g) aG/aI0 < 0 for al < 01 < 1. When plotted against 01, G is an inverse U-shaped curve that takes on a maximum value of a, at 01 (figure 4.1). Therefore al is the critical value of 0G marking off the two phases of G. The maximum value of G, when 01 is equal to al, is given by: (4.8) G = 2a-1. In figure 4.1 the emergence of a privileged splinter group out of a homogeneous labor force is represented by movement along one 154 THE INEQUALITY OF FAMILY WAGE INCOME

Table 4.11. Numerical Example of the Gap between the Relative Value of the Education Characteristic for a Privileged Group and That for a Less Privileged Group (values of s)a

V2 for privilegedgroup Twelve Nine years years Fourteen Sixteen Six years (junior (senior years years VI for less (primary high high (technical (university privilegedgroup school) school) school) school) or over)

Six years (primary school) 0 0.200 0.333 0.400 0.455 Nine years (junior high school) - 0 0.143 0.217 0.280 Twelve years (senior high school) - - 0 0.077 0.143 Fourteen years (technical school) - - 0 0.666 Sixteen years (university or over) - - - 0

- Not applicable. Source: Constructedby the authors. a. s = V* -V*. of the curves from the point U, where 0o is equal to 1, to the left toward the origin, where ol is equal to zero. This movement indicates that the fraction of labor in the underprivileged group [01] is declining. Consider the level of education as an illustration. The value of s between two education characteristics is given in table 4.11, where the years of education are indicated in the headings. For example, the value of s is 0.2 between junior high school, for which /2 is 9, and primary school, for which VI is 6. Starting from the point U in the curve relevant to an s of 0.2 in figure 4.1, a turning point is reached at point T. Thus popularization of junior high school education will first cause the inequality [Gi] to increase to a maximum of 0.10, at which point the proportion of workers with junior high school education has increased to about 45 percent. Notice when the value of s is higher-such as the s of 0.45 between university and primary education-that popularization of higher education will raise the labor characteristic Gini much faster-in INEQUALITY OF INCOME OF INDIVIDIUAL WAGE EARNERS 155 this example to a peak value of 0.24 at point T'. But the turning point [T'] will arrive sooner, when about 38 percent of workers have university education. The emergence of an underprivileged splinter group out of a homogeneous labor force is represented by movement along one of the curves from the origin, where 01 is equal to zero, to the right toward the point U, where 01 is equal to 1. This movement indicates that the fraction of labor in the underprivileged group is increasing. The entry into the labor force of females and young workers under 25 are typical instances of this pattern. When such an inferior group is formed, inequality precedes equality, just as for the formation of a superior group. But when an inferior group is formed, a higher value of s will not only cause the labor characteristic Gini to increase faster, but will also postpone the turning point to a higher value of 01. The skewness of these curves shows the basic asymmetry between the formation of privileged and underprivileged groups. Notice when the value of the sex characteristic is indexed by zero for females and by 1 for males that the value of s for sex is the maximum-that is, it is equal to 1. Equation (4.6g) then is reduced to a limiting and special case in which G is equal to 01, a relation represented by the 450 line OA. Therefore the sex Gini is precisely the fraction of female workers in the labor force; it continuously increases with increasing rates of female participation. It can be seen from the foregoing discussion that the labor characteristic Gini EGi] measures inequality in a special sense. Whether a homogeneous group is inferior or superior, a low value of Gi means that the number of workers in that group is either very small and socially insignificant or very large and common. The first instance would be indicated by a small 01; the second by a large 01. A low Gi also means that the superiority or inferiority of the homogeneous group is not very pronounced, which would be indicated by a small s. Vague as it might seem, the values of Gi consequently measure certain properties of a group of workers-properties which common sense would regard as underlying causes of inequality.

Labor characteristic weight The labor characteristic Gini EGi] measures the degree of nonhomogeneity of labor. Whether Gi is a principal cause of inequality of wage income depends upon the influence of that characteristic 156 THE INEQUALITY OF FAMILY WAGE INCOME

on the wage rate. Suppose that the male premium [a,] is zero-that is, there is no difference between the male and female wage rates. Then sex cannot be a principal cause of inequality of wage income, regardless of the magnitude of Gi. The labor characteristic weight [E1]measures the relative wage-earning power associated with a labor characteristic. Notice that the regression coefficients [ai] of equation (4.1) are computed from the primary data for the wage pattern [W] and the labor characteristic pattern [Xi] of equation (4.4). The primary data for the wage pattern [W], the sex characteristic pattern [X1], and the education characteristic pattern [X2] in table 4.9 lead to the following regression equation:

(4.9a) W = a. + aizx + a2x2 + 8, where

(4.9b) a. = -1, a1 = 2, and a2 = 3. When the r values of Xi are substituted into the regression equation (4.1), a column of error terms [86 = col(61, 82, . . . , an] is determined.

(4.10a) W = a + aix + a2X2 ... + arXr + 5,, where

(4.10b) a. = col(a., a0, . .. , a0) and

(4.10c) 61+ + *.2 * * + an = 0 The computation of 6, for the numerical example in table 4.9 appears in the right-hand columns. Notice when the regression coefficients are estimated by the method of least squares that the sum of all values of bi is zero (see equation [4.10c]). Because of this property the mean values of all column vectors in equation (4.10a) have the followingrelations:

(4.11a) W = a. + aljl + a2t2 + ... + asxt, where

(4.1lb) W = (W1 + W2 + . .. ± W.)/n and

(4.11c) xi = (Zil + Xi2 + Xi3 + ... + xn)/n, and a. (4.11d) 1 = + 1 + 2... + ' T , where

(4.11e) oi = ajiv/iB. (i = 1, 2, . , r.) In equation (4.1lb) W is the mean wage income; in equation (4.11c) xi is the mean value of the ith characteristic. For example, if x2 is measured in years of formal education, then X2 is the average years INEQUALITY OF INCOME OF INDIVIDUAL WAGE EARNERS 157 of education for the n workers. The labor characteristic weights [0j] are defined in equation (4.11e). Because the product of the education premium and the average years of education [aiti] represents the average contribution of education to the wage rate, the education characteristic weight is a measure of this contribution as a fraction of the average wage rate. For a typical term 4iRiGi in equation (4.3), it can thus be seen that a labor characteristic Gini [Gi] cannot make a heavy contribution to the inequality of wage income unless the labor characteristic weight [Ei] is large." The values of the labor characteristic weights are given in table 4.9: ol is 0.125; 02 is 1.03125. When a higher value of a variable [xe] corresponds to higher earning power, the regression coefficient [ai] is positive. Consequently the values of 4i are nonnegative. It can nevertheless be seen from equation (4.11d) that the r values of (i do not form a system of weights unless the regression constant [a0] is equal to zero. Because a. is negative in the numerical example, the values of oi add up to more than 1. The rank-weighted error term [A] in equation (4.3) is defined as follows:

(4.12a) A = (j.11. + i2 62 . ± jaJ.)/ I, where (4.12b) ji = i/(l + 2 + ... + n) and (i = 1, 2, ... ,n)

(4.12c) l + i2 ... + j,, = 1. The values of ji in equation (4.12b) are relative ranks used as a system of weights. Therefore A is the rank-weighted error expressed as a fraction of the average wage [W]. It measures the importance of the error term in equation (4.3). In view of equation (4.10c) A can be positive or negative. The computation of A as being equal to 0.0047 is shown in table 4.9.

Labor correlationcharacteristic The contribution of a labor characteristic, such as education or sex, to the inequality of wage income depends not only on the labor characteristic weight [+X] and the labor characteristic Gini [Gi],

11. Notice that (Xi, W) is a mean point on the regression line. Thus 4. is the elasticity of w with respect to X, at the mean point. To illustrate: 2 for education is the percentageincrease in the averagewage rate when the averagenum- ber of years of educationincreases by 1 percent. 158 THE INEQUALITY OF FAMILY WAGE INCOME but also on the extent to which the values of a characteristic are correlated with wage income. Assume that the pattern of wage income of five workers is W = col(10, 12, 18, 25, 30) and the years of formal education are given by two alternatives, X2 = col(6, 6, 9, 12, 14) and X2 = col(14, 9, 12, 6, 6). For the first alternative, workers with higher income receive a higher education-that is, W and Xl are highly and positively correlated. For the second alternative, the opposite is true. Workers with higher income receive a lower education-that is, W and X22are negatively correlated. The higher income in the second alternative is the result of such other labor characteristics as sex and age; education in fact contributes to the equality of wage income, not to its inequality. Observe that the value of the labor characteristic Gini [EG] is the same for X2 and X22.Thus the impact of education on the inequality of wage income depends not only on the labor characteristic Gini [G], but also on the correlation characteristic [Ri]. Other things being equal, a high positive value of Ri indicates that the ith characteristic contributes more to the inequality of wage income than to its equality. If Ri is negative, the ith characteristic contributes to equality, not to inequality Esee equation (4.3)]. When the primary data are given for a particular labor characteristic according to equations (4.4a) and (4.4b), the labor correlation characteristic is computed as follows: (4.13a) Ri = Ri(W, xi) = 0i/lG, where

(4.13b) 0i = 2ui/n - (n + 1)/n, where

(4.13c) i% = r(xill/si) + r2 (xi 2/si) + ... + rn(xin/s8), where

(4.13d) Si = xi1 + xi2 + . . . + xin and ri is the wage income rank of the ith worker. The computation or RJ and R2 is indicated in table 4.9. Note that the education characteristic has a perfect rank correlation with wage income, giving

R 2 a value of 1. In general the labor correlation characteristic ERi] is that fraction of the labor characteristic Gini [Gi] which can be explained by the variation of wage income or the correlation characteristic between W and X,.12

12. In part two Ci is referred to as the pseudo Gini coefficient, and R, is the ratio of the pseudo Gini coefficient to the Gini coefficient. See chapters eight and nine in part two. INEQUALITY OF INCOME OF INDIVIDUAL WAGE EARNERS 159

Empirical analysis Decomposition equation (4.3) was applied to the data for 1966 (table 4.12). The decomposition was carried out separately for rural areas, towns, and cities to yield the labor characteristic weights [Es], the labor characteristic Ginis [G3I, and the correlation charac-

Table 4.12. Decomposition Analysis of the Inequality of the Wage Rate, by Location and Labor Characteristic, 1966

Variable Notation Rural area Town City

Labor characteristic weight Sex Oi 0.3536 0.3486 0.3123 Education 02 1.4952 1.1167 0.6564 Age 03 0.5025 0.5360 0.7092 Family income 04 0.1979 0.1421 0.2151

Labor characteristic Gini Sex GI 0.3304 0.2363 0.2190 Education G2 0.8092 0.5584 0.5506 Age G3 0.5816 0.5798 0.5622 Family income G4 0.5020 0.4820 0.4404

Labor correlation characteristic Sex R1 0.6338 0.8819 0.6932 Education R2 0.1036 0.3281 0.3382 Age R3 0.1850 0.4129 0.3131 Family income R4 0.9693 0.5477 0.4301

Contribution term Sex ,R1G1 0.0740 0.0726 0.0474 Education k2R2G2 0.1253 0.2046 0.1222 Age 413R10 0.0541 0.1283 0.1248 Family income 04R4G4 0.0963 0.0375 0.0407

Wage Gini G. 0.6108 0.5434 0.4876 Explained wage Gini 0G 0.3497 0.4430 0.3351 Rank-weighted error term A 0.2611 0.1004 0.1525

Sources: Calculated from tables 4.20-4.27 appended to this chapter. 160 THE INEQUALITY OF FAMILY WAGE INCOME

Figure 4.2. The Wage Gini and the Explained Portion of the Wage Gini, by Location, 1966

1.0 _

430.5 _ 43 peren 0.5 ppercent percent 3110.48 p~ercent

82 7Bercent 69 percent ~~~~~~percent

Rural Town City area

2Wage (Gini [G] Explained portion of the wage Gii [Gi ]

Source:Table 4.12.

teristics [Ri]. The factor contribution terms [0&RjGj] measure the contribution of various labor attributes to the degree of inequality of wage rates. At the bottom of table 4.12 are shown the Gini coefficient of the wage rate [GIj, the sum of the four factor contribution terms [Gi], and the rank-weighted error term [A] which is equal to G. minus OG. Figures 4.2 and 4.3 graphically summarize the essential information in this table. The shaded areas in figure 4.2 represent the explained wage Gini [&T-1-that is, that portion of the wage Gini that can be explained by the four characteristics traced in this analysis. The shaded and unshaded areas together represent the wage Gini EGW].It can be seen that the inequality of the wage rate [Gm] consistently declines from 0.61 for traditional rural areas to 0.54 for semimodern and semirural towns and 0.49 for modern cities. These magnitudes indicate, at least for 1966, that modernization was not accompanied by the increased wage inequality which the Kuznets hypothesis INEQUALITY OF INCOME OF INDIVIDUAL WAGE EARNERS 161 would suggest. The explained wage Gini [O.] accounted for 57 percent of the wage Gini [Gm] for rural areas, 82 percent of that for towns, and 69 percent of that for cities. The rank-weighted error terms respectively accounted for 43 percent, 18 percent, and 31 percent of the wage Gini. In other words, the influence of sex, education, age, and family income can explain only about 70 percent of the causes of wage-rate inequality. In this analysis 30 percent cannot be accounted for by these characteristics."3 By comparing rural areas, towns, and cities, an inverse U-shaped pattern can be observed in the proportion of the explained inequality [&G,,GJ. That proportion rises from 57 percent to 82 percent and then declines to 69 percent. Such a pattern suggests that other, unidentified causes of the inequality of wage rates are more pronounced in rural areas and large cities than in towns. In towns, however, sex, education, age, and family influence together constitute a set of causal factors which can adequately explain the inequality of wage rates. The following analysis concentrates on this explained portion of wage- rate inequality-that is, it concentrates on G., not on G,. The percentage contributions of sex, education, age, and family income to explained wage-rate inequality [GW] are shown in figure 4.3. The education characteristic, with a simple average of 39 percent for the three locations, makes the largest contribution. The age characteristic contributes 28 percent, the sex characteristic 17 percent, and the family-influence characteristic 16 percent. Thus education and age characteristics together account for about two-thirds of the explained inequality of the wage rate. Because the productivity of workers with varying educational qualifications and experience (proxied by age) is different, the contribution of these two characteristics to wage-rate inequality can be viewed as rational or warranted. In contrast, the productivity differences of workers of different sex and family background are not as apparent. The contribution of these two factors to inequality, unrelated as they are to productivity, can thus be viewed as irrational or unwarranted. The substantial volume of unwarranted causes, which accounted for about one-third of the explained inequality, suggests that institutional discrimination against women

13. The unexplained portion of G,. could be further reduced by considering an additional dimension of the quality of labor, the job or occupational characteristic. 162 THE INEQUALITY OF FAMILY WAGE INCOME

Figure 4.3. Percentage Composition of Factor Contributions, by Location, 1966

100

-'50 ;:4SH~~~~~~~~4

O , .'.,-. '9 ' . 111 Rural Town OiLy area

Sex (decreasing) [01R,G,] Education (inverse U-shaped)[E2R 2G2]

EAge (increasing) [k3RaG3] gFamily income (U-shaped) tk 4R4G4]

Source: Table 4.12.

and in favor of members of wealthy families was important in labor markets. Institutional discrimination declined from 49 percent for rural areas to 26 percent for cities. In other words, institutional discrimination was about twice as strong in rural areas as it was in cities. This evidence thus supports the assumption that modernization tends to reduce the discrimination against females and members of poorer families. Notice moreover that family influence was relatively more important than sex discrimination in rural areas, but that this ranking was reversed in cities. It seems that modernization removes the bias of family influence faster than that of sex discrimination. The contribution of the education characteristic to wage-rate inequality [&E]was 36 percent for rural areas, 46 percent for towns, and 36 percent for cities. It thus exhibited something of an inverse U- shaped pattern. The age characteristic, with values of 15 percent for rural areas, 29 percent for towns, and 39 percent for cities, never- INEQUALITY OF INCOME OF INDIVIDUAL WAGE EARNERS 163

Figure 4.4. Composition of the Contribution of Education to Explained Inequality, by Location, 1966

1.5 130O

1.12

1.0 1

08S1

0.65

0.5 -

area

~~EducatzonGun [02] Education correlation Education weight .... to ....Scharacteristic [R,].... [(]

Source: Table 4.12.

theless presented an unmistakable increasing pattern. Age and experience together accounted for more wage-rate inequality in cities than in rural communities. In the following discussion an attempt will be made to explain why these two warranted characteristics of age and education exhibited such a pattern. Then the other two characteristics will be discussed.

THE CONTRIBUTION OF EDUCATION TO INEQUALITY. The data underlying the analysis of the contribution of education [X2 R2C,] to wage-rate inequality [Gm] is graphically summarized in figure 4.4. 164 THE INEQUALITY OF FAMILY WAGE INCOME

Based on the survey results for 1966, the education Gini [G2] was 0.81 for rural areas, 0.56 for towns, and 0.55 for cities. The education weight [02] was 1.50 for rural areas, 1.12 for towns, and 0.65 for cities. These declining values associated with increased urbanity reflect the high number of educated workers in cities. Both 02 and G2 contributed to the reduction of 02R2G2 for semiurban and urban areas. Education's contribution to overall wage-rate inequality exhibited an inverse U-shaped pattern for the three locations primarily because R2 increased as both 42 and G2 declined. The correlation characteristics [R 2] were 0.10 for rural areas, 0.33 for towns, and 0.34 for cities. In other words, the wage rate was correlated with educational qualifications to a much higher degree in cities than in rural areas. The economic interpretation of this evidence is that the wage rate in cities reflects formal educational qualifications of workers with a higher degree of sensitivity than it does age, sex, and other unspecified characteristics. This pattern is precisely what would be expected in a commercialized urban environment in which labor markets tend to be somewhat more perfect.

THE CONTRIBUTION OF AGE TO INEQUALITY. As was seen in figure 4.3, the contribution of age [03R]Gs] to inequality [O.] was least in rural areas and greatest in cities. Although the age Gini was about 0.57 for the three sectors, the weighted correlation characteristic [43R3]was larger in cities than in rural areas, mainly because the correlation of age with wage income ER3 ] was much higher in towns (figure 4.5). This evidence indicates that older workers, who as- sumedly were more experienced than their younger counterparts, participated much more in the urban work force than in the rural. The value of q53R3 was about 0.22 for both towns and cities. But the contribution of age to inequality was greater in cities than in towns- 0.39 compared with 0.29-primarily at the expense of the contribution of education, which was greater in towns than in cities-0.46 compared with 0.36. Thus age and experience began to overtake education as the most important factor contributing to the inequality of the wage rate in the cities. The reason probably is that work experience counted for relatively more in the industrial complexes of large cities. By comparing rural areas and urban areas, three tendencies can be detected in the two warranted characteristics of education and age. First, the education Gini was lowest in cities and highest in rural areas, but the age Gini was highest in cities and lowest in rural INEQUALITY OF INCOME OF INDIVIDUAL WAGE EARNERS 166

Figure 4.5. Comnpositionof the Contribution of Age to Explained Inequality, by Location, 1966

1.0

0.71

0.58 0-M 0.54 0X56

Rural Town Ct area

4ge correlatin j:Age Girni [0,] ~characteri,sticER,] WAge weight [4o]

Soure:. Table 4.12.

areas. This pattern means that, when workers with higher formal education become more abundant, the experienced worker begins to gain in importance. In figure 4.1 the rural, town, and city situa- tions for the education Gini are represented by the points R', T', and C' on the increasing portion of the inverse U-shaped curve (remember that the formation of a privileged group is indicated by movement from the point 01 to the left toward the origin). Thus, when the labor force is modernizing, the development of education attributes precedes that of experience attributes. Although the age characteristic still contributes to inequality, the education characteristic begins to contribute to equality. Second, the education weight [+2] was lowest in cities and highest in rural areas, but the age weight [¢3] was highest in cities and lowest in rural areas. Con- sequently, during modernization, age begins to count more heavily than education in production. Third, the correlation characteristic 166 THE INEQUALITY OF FAMILY WAGE INCOME

[R3] was higher in semiurban and urban areas than in rural areas. This evidence suggests that the better developed labor market is more sensitive in rewarding both education and experience in the commercialized milieu of large cities.

THE CONTRIBUTION OF SEX TO INEQUALITY. As already seen, institutional discrimination, particularly that against women, was weaker in cities than in rural areas. The sex contribution term [EOR0Gl]was 0.074 for rural areas and 0.047 for cities (see table 4.12). Of the factors of this term, the sex Gini [Ga] really is equivalent to the female participation rate. The sex correlation characteristic R,1] represents the correlation between the wage rate and the maleness of workers. For example, if the pattern of the wage rates for five workers is given by ($10, $20, $35, $50, $100) and the sex of these workers is given by (0, 0, 0, 1, 1), the highly positive correlation [E1] means that male workers get the better paid jobs. Conversely, if the sex pattern of these workers is given by (1, 1, 0, 0, 0), the negative correlation reveals that females get the better paid jobs. A high value of R1 therefore is equivalent to job- availability discrimination: that is, the more a job pays, the less it will be available to females. The sex weight [E1]reflects the male premium in the wage structure: the higher the value of 41, the higher the degree of discrimination against women. The contribution of sex to inequality was about the same for towns and rural areas. The reason for this pattern is that the higher urban R1 canceled the lower urban G1. More concretely, the female participation rate in towns, proxied by a G0of 0.23, was lower than that in rural areas, proxied by a G1 of 0.33 (figure 4.6). At the same time, men were getting more of the better paid jobs in towns, proxied by an R1 of 0.88, than in rural areas, proxied by an R1 of 0.63. In cities, all three factors work in the relative favor of female workers. Compared with their counterparts in towns, female workers in cities had a slightly lower participation rate, obtained more of the better paid jobs, and benefited from a lower male premium.

THE CONTRIBUTION OF TOTAL FAMILY INCOME TO INEQUALITY. As with sex discrimination, the wage-rate favoritism for members of wealthier families was lower in urban areas than in rural areas. The family-influence contribution term [E4Rf4 4] was 0.096 for rural areas, 0.037 for towns, and 0.041 for cities. The family-influence INEQUALITY OF INCOME OF INDIVIDUAL WAGE EARNERS 167

Figure 4.6. Composition of the Contribution of Sex to Explained Inequality, by Location, 1966

1.0 0.88

0.69 0.63

0.5-

0.33 0.353.8 0.31 oLA 0.23 ~~0.22

Rural Town City area

,,Sex correlation E]Sex Gini EGI] characteristic X IR, Sex weight [o,'

Source: Table 4.12.

Gini [G4 ] simply is the Gini coefficient measuring the degree of inequality of total family income. The family-influence weight ['4] measures the wage advantage of members of relatively wealthy families: the higher the value of 04, the greater the wage-rate discrimination. The family-influence correlation characteristic [R4 ] measures the extent to which wealthy families can secure better paid jobs for their members through nepotism. In effect it is a measure of job-availability discrimination. In 1966 total family income was distributed most equally in cities and least equally in rural areas. The family-influence Gini [G4] was 0.44 for cities, 0.48 for towns, and 0.50 for rural areas (figure 4.7). It would also appear that the market mechanisms associated with increasing urbanity gradually weaken the role of special influence in the award of high- salary jobs to workers. The correlation characteristic associated with 168 THE INEQUALITY OF FAMILY WAGE INCOME

Figure 4.7. Coinposition of the Contribution of Family Influence to Explained Inequality, by Location, 1966

1.0- 0.96

o 4

0.5- 0_44 0_43

Rural Town City area

Family influence Family influence correlation Family influence LGini [G4 ] E characteristic FR4] t weight [E0]

Source: Table 4.12.

family influence [R 4] was 0.96 for rural areas, 0.54 for towns, and 0.40 for cities. These factors help explain the decline of nepotism as a form of institutional discrimination in the commercialized milieu of urban areas.

Inequality of Family Wage Income: Third-level Analysis

If a family has more workers or family members with higher wage-earning power, it will clearly tend to have a higher total wage income. Assume that there are r types of worker with a pattern of wage rates given by (wi, w2, . .. , wr). Suppose further that there are n families. Then let the pattern of total family wage income of these families be denoted by W = col(W1 , W2, ... , W.). Suppose INEQUALITY OF FAMILY WAGE INCOME 169 that the ith family has xij workers of the jth type. Then:

(4.14a) W = w1X1 + w2X2 + . . . + wrXr, where

(4.14b) Xi = CoI(xli, X2i, . .. , xi) and (i = 1, 2, ... , r) (4.14c) WI < W2 < ... < W. . The column vector Xi stands for the pattern according to which the workers of the ith type are distributed among the n families. Notice in expression (4.14c) that the n families are arranged in a monotonically increasing order: in total wage income, the first family is the poorest, the last family wealthiest. Let G. denote the Gini coefficient of the distribution of wage income [W] and measure the degree of inequality of family wage income. Make use of a decomposition equation of the following form:

(4.15) G. = 0¾R1 G1 +±2R 2G2 + ... + 0,RrGr. In equation (4.15) G. measures the degree of inequality of total family wage income. The term 4iRiGiwill be referred to as the contribution of workers of the ith type to inequality. The Gini coefficient EG[] of the labor characteristic vector EXi] measures the inequality of distribution of workers of the ith type among families. It will be referred to as the family membership Gini of the ith type. The term 4i is defined as follows:

(4.16a) W = wltl + w2x2 + . WrXr, where

(4.16b) W = (W 1 + W 2 ±+ ... + W.)/n and

Xi= (Xli + X2i + ... + x.i)/n, and

(4.16c) 1 = 1++ 0± . + 4¾, where

(4.16d) 4¾ = w,.ttW. (i = 1, 2, ... ., r) In equation (4.16b) W is the average wage income of families, and z, is the number of workers of the ith type per family. Thus 4¾ is the fraction of wage income per family earned by workers of the ith type. Call this fraction the wage income weight. The degree of family wage-income inequality [Gw] can also be affected by the correlation characteristic between W and Xi. Suppose there are five workers with a pattern of Ph.D. membership given by (0, 0, 1, 2, 1). As would be expected, these highly paid workers are concentrated among the wealthy families: that is, the correlation between W and Xi is high and positive. If the pattern of Ph.D. 170 THE INEQUALITY OF FAMILY WAGE INCOME membership were instead given by (1, 1, 2, 0, 0), the family membership Gini would be the same, but the negative correlation between W and Xi would obviously contribute to the equality of family wage income, not to its inequality. When the wage rates of r types of worker are arranged in a monotonically increasing order

given by (w, < W2 < ... < wr), the first type of worker is the lowest paid and the last type of worker is the highest paid. With such a pattern, the low-paid workers would be expected to be concentrated among the poor families, leading to a negative correlation between W and Xi; the high-paid workers would be expected to be concentrated among the wealthy families, thus leading to a positive correlation between W and Xi.

Empirical analysis For purposes of empirical analysis at the third level, forty types of workers can be identified for the regression equation (4.2). The number 40 is the product of the number of values assumed by the sex, education, and age characteristics. Sex has two values: M for male, and F for female. Education has five values: L for primary school; I for junior high school; H for senior high school; T for technical school; and U for university or over. Age has four values: i for under 25; 2 for 25-45; 3 for 45-60; and 4 for over 60. Thus the combination of attributes embodied by a homogeneous group of workers can, for example, be denoted by Ml1LI,which would indicate male workers under 25 having primary school education, or FT3, which would indicate female workers aged 45-60 and having technical school education. To simplify the analysis, the family influence variable is not used here. Wage rates for the various types of workers in 1966 were computed from the following equation:

(4.17a) w = a. + a1 x1 + a2x2 + a3x3, where

(4.17b) a, = 13.61, a1 = 5.277, a2 = 1.512, a3 = 3.486 and

(4.17c) x1 = (0, 1), x2 = (6, 9, 12, 14,16), X3 = (1, 2, 3, 3). [sex] [education] [age] The values of the regression coefficients [ai] in equation (4.17b) were computed as the average of the rural, town, and city coefficients of table 4.6, weighted by the sample sizes indicated there. INEQUALITY OF FAMILY WAGE INCOME 171

When the values of xi in equation (4.1 7c) are substituted into equation (4.17a), the wage rates [wi] can be computed (table 4.13). Notice that the wage rate for females under 25 with primary education (FL1) becomes negative. The reason is that the term representing the influence of total family income [a4 x4 ] in equation (4.2) has been omitted from equation (4.17a). Notice also that the wage rates in table 4.13 are arranged in a monotonically increasing order. And because three categories contain no workers (Ff4, FH4, and FT4), there are thirty-seven wage rates, not forty. The lowest paid workers were females with primary education under 25 (FL1); their wage rate [w,] was -3.212. The highest paid workers were males with university education aged 45-60 (MU3); their wage rate [w37] was 20.557. For each category the family membership Gini EGj] reveals the degree of inequality of family ownership of the workers of the ith type. For example, suppose that there are five families and the ownership pattern of female workers with university education aged 25-45 (FU2) is given by (0, 0, 1, 2, 2). The two poorest families own no workers in this category; such workers are concentrated among wealthy families. The family membership Gini shows the degree of inequality of the ownership pattern of workers. For each category, Ri is the correlation characteristic between the ownership pattern and total family wage income. A high and positive Ri indicates that the ownership of workers of this type is concentrated in families with higher total wage income; a negative Ri, in families with lower total wage income. To compute the wage income weight [4i] for every category, the following procedure was used. An estimated pattern of total family wage income pattern [W = col(Wl, W2, .. , W,)] was computed from equation (4.14a) to yield:

(4.18a) W = z 1XI + 72 2X 2 + ... + I%VVX37,

(4.18b) W = Wl1t + iV2 2 +.+ .. ±w 1 X 3 7 , and

(4.18c) 1 = 01 + 02 + ... + 037, where

(4.18d) i = wix,/W.

In this estimation the wage rates given by (wii, iiV2,.. ., 137) are first estimated from the regression coefficients in table 4.6. Thus the estimated wage income pattern [WV] differs from the actual pattern. The term oi represents the wage income per family earned 172 THE INEQUALITY OF FAMILY WAGE INCOME

Table 4.13. Wages Rates, Family Membership Ginis, and Other Variables for Thirty-seven Categories of Workers, 1966

Male

Level of education Nota- Under 25 25-45 46-60 Over60 and variable tion years years years years

Primary school (ML1) (ML2) (ML3) (ML4) Wage ratea Wi W4 = W=o = W187 2.065 5.551 9.037 9.037 Family membership Gini 0 0.125 0.110 0.030 0.340 Correlation characteristic R -0.080 -0.636 0.667 -0.674 Mean of x 0.164 0.426 0.154 0.016 Wage income weight s 0.039 0.272 0.160 0.017 Contribution term ORO -0.0039 -0.019 0.0032 -0.0009

Junior high school (MI1) (MI2) (MI3) (M14) Wage rate wi W9 = wV6 = Us2 5 = W24 = 5.521 9.007 12.493 12.493 Family membership Gini a 0.372 0.380 0.350 0.730 Correlation characteristic R 0.194 0.655 0.886 0.425 Mean of x 0.021 0.078 0.023 0.001 Wage income weight 4 0.013 0.081 0.033 0.001 Contribution term bRG 0.0009 0.0202 0.0102 0.0003

Senior high school (MH1) (MH2) (MH3) (MH4) Wage rate wi W15 = W23 = W32 = W31 = 8.977 12.463 15.949 15.949 Family membership Gini G 0.350 0.380 0.543 0.880 Correlation characteristic R -0.266 0.942 0.996 0.318 Mean of x 0.027 0.108 0.039 0.0004 Wage income weight q0 0.028 0.155 0.072 0.001 Contribution term ORO -0.0026 0.0555 0.0389 0.0003

Technical school (MT1) (MT2) (MT3) (MT4) Wage rate wi W21 = W28 = W35 = W34 = 11.281 14.767 18.253 18.253 INEQUALITY OF FAMILY WAGE INCOME 173

Female

Under 25 25-45 45-60 Over 60 Nota- Level of education years years years years tion and variable

(FLI) (FL2) (FL3) (FL4) Primary school Wi W1 = W3 = W8 = W7 = Wage ratea -3.212 0.274 3.760 3.760 Family membership 0.130 0.190 0.280 0.660 G Gini Correlation -0.769 -0.842 -0.9253 -0.764 R characteristic 0.196 0.147 0.0361 0.005 x Mean of x 0.073 0.005 0.016 0.002 ( Wage income weight 0.0073 -0.0008 -0.0042 -0.0010 fRG Contribution term

(Fli) (F12) (F13) (F14) Junior high school w2 w 6 = w13 = - wi Wage rate 0.244 3.730 7.216 Family membership 0.240 0.670 0.770 - G Gini Correlation 0.838 0.910 -0.088 - R characteristic 0.018 0.012 0.001 - x Mean of x 0.0005 0.005 0.001 - k Wage income weight 0.0001 0.003 -0.0001 - cRG Contribution term

(PHI) (FH2) (FH3) (FH4) Senior high school W5 = W12 - W20 = - wi Wage rate 3.700 7.186 10.672 Family membership 0.400 0.680 0.680 - G Gini Correlation 0.645 0.985 0.206 - R characteristic 0.017 0.012 0.003 - x Mean of x 0.007 0.010 0.004 - c Wage income weight 0.0018 0.0067 0.0006 - ORG Contribution term

(FT1) (FT2) (FT3) (FT4) Technical school

Wii = wig = W26 = - W; Wage rate 6.004 9.490 12.948 (Tablecontinues on thefollowing pages) 174 THE INEQUALITY OF FAMILY WAGE INCOME

Table 4.13 (Continued)

Male

Level of education Nota- Under 25 25-45 45-60 Over 60 and variable tion years years years years

Family membership Gini G 0.780 0.702 0.850 0.970 Correlation characteristic R 0.218 0.944 0.953 1.000 Mean of x 2 0.002 0.009 0.004 0.0004 Wage income weight 0 0.003 0.015 0.008 0.001 Contribution term sRG 0.0005 0.0099 0.0065 0.001

University or over (MU1) (MU2) (MU3) (MU4) Wage rate wi W27 = Ws3 = W37 = W36 = 13.585 17.071 20.557 20.557 Family membership Gini G 0.846 0.630 0.569 0.870 Correlation characteristic R 0.366 0.968 0.967 0.840 Mean of x 0.002 0.030 0.018 0.002 Wage income weight q 0.003 0.059 0.043 0.005 Contribution term pRG 0.0009 0.0360 0.0237 0.0037

- Not applicable. Sources: Calculated from tables 4.20-4.27 appended to this chapter. a. In thousands of N.T. dollars; i is the wage rank. by workers of the ith type expressed as a fraction of the estimated average family income [EWJ].The values of 4i add up to one. For all thirty-seven categories, the contribution of workers of the ith type to inequality was 0.2060 (see table 4.13). This value is the Gini coefficient of total family wage income [EOT]for the estimated wage pattern [EW] of equation (4.18a) .14 The values of oi, Ri, and OiRiGi are plotted against the wage rate in figures 4.8-4.11. In figure 4.8 the contribution of the thirty-seven grades of labor [FiRiGi] to the inequality of total family wage income [GE] is

14. We are not concerned in this section with the difference between the true G, and G,,-that is, with the unexplained portion of G,, measured by G.,, -G. INEQUALITY OF FAMILY WAGE INCOME 175

Female

Under 25 25-45 45-60 Over 60 Nota- Level of education years years years years tion and variable

Family membership 0.780 0.890 0.930 - G Gini Correlation -0.474 0.787 0.752 - R characteristic 0.001 0.002 0.0004 - x Mean of x 0.001 0.002 0.001 - 4 Wage income weight -0.0004 0.0014 0.0007 - 4RG Contribution term

(FU1) (FU2) (FU3) (FU4) University or over W14 = W22 = W30 = W29M wi Wage rate 8.758 12.244 15.730 15.730 Family membership 0.850 0.820 0.920 0.960 G Gini Correlation 0.804 0.915 1.000 0.903 R characteristic 0.002 0.004 0.0013 0.0004 t Mean of x 0.002 0.006 0.002 0.001 4 Wage income weight 0.0014 0.0045 0.0018 0.001 4RG Contribution term

measured on the vertical axis. The grade of a particular type of labor corresponds to its rank in the wage-rate structure and is measured on the horizontal axis. The nine types of labor below the horizontal axis-that is, those having a negative 4iRiGi-contribute to equality, not to inequality. They constitute the so-called marginal labor force: the poorly educated male and female workers who are either very young and have little work experience or are very old and near retirement. The exception to this characterization is the category of poorly educated male workers aged 25-45 (ML2) who constitute the bulk of the unskilled labor force. The dotted horizontal line aa' divides the types of workers who contribute to inequality into two groups. Those above the line essentially are male workers in their prime age-that is, 25-60. The exceptions are highly educated females in their prime age (FU2 and FH2)-that is, 25-45. This group, which can be referred to as 176 THE INEQUALITY OF FAMILY WAGE INCOME

Figure 4.8. Contribution to Family Wage Income Inequality, by Labor Grade, 1966

0.015 - MH2 MH3 *MU2 M U3 M12 MI3 MT2 0.010

MU1 FH2 MT3 * a MTi 0.005 _ a ~~~~~~~*FU2 FI2 MLS MI4 MH4 M a' * MU4

aFHI . FUI FT2 IT4 Mu PU. FH3 PT3 FUM4 FII **U

. F13 10 15 FL4 * FT1 Wage rate [wi]

* MH1 (thousands of N.T. dollars) MLI * FL3 . ML4 -0.005 -

FL1 *FPI,

-o.oiLa

Source: Table 4.13.

the prime age group, makes a heavy contribution to inequality. It accounts for more than 100 percent of the inequality of family wage income (0.2135/0.2060 = 1.036). Its contribution adds up to more INEQUALITY OF FAMILY WAGE INCOME 177 than 100 percent because the marginal labor force contributes to equality. Given the foregoing conclusion, a sharp distinction can be drawn between two issues which are sometimes confused: the degree of inequality of family wage income; the welfare of the marginal labor force. Government relief or welfare measures-for example, minimum wage legislation-may represent attempts to help the marginal labor force, but they do little to resolve the basic inequality of family wage income. In other words, even if the welfare problem were solved, the degree of inequality of total family wage income would remain essentially unchanged. The reason for this outcome is that the inequality of family wage income is a condition that centers mainly around workers in the prime age group. The correlation between the wage rate, or labor grade, and its contribution to inequality is significant and positive (see figure 4.8). It can be imagined that the labor force in a traditional society is homogeneous and that the wage rate is low. Industrialization then brings about wage increases as the labor force begins to be differentiated. The impact of such modernization is mainly directed at the prime labor group. The emergence of high-grade laborers and the increase in their number represent the major causes of family wage-incomeinequality. The positive correlations in figures 4.9 and 4.10 explain the positive correlation between Wi and &iRiGi.First, the positive correlation between the wage rate [We] and the degree of inequality of family ownership of workers of various grades [Gi] in figure 4.9 means that low-grade laborers are more evenly distributed among families than are laborers of higher grades. Put differently, as the higher grade laborers come into being, they are acquired by a mi- nority of families. Second, the positive correlation in figure 4.10 between the wage rate [Wi] and the degree of correlation between total family wage income and family ownership of labor [Ri] suggests that the laborers of higher grades are acquired by wealthy families that have a higher total wage income. The inequality of family ownership of high-grade laborers thus rnust be regarded as the most imnortant cause of family wage-incomeinequality. Economic development can affect the inequality of family wage income through another set of factors which are purely economic. Consider this example. The mean values of the number of workers of various grades per family are denoted by xi (see table 4.13). If N is the total number of families-N is equal to 2,379 in table 4.13 178 THE INEQUALITY OF FAMILY WAGE INCOME

Figure 4.9. Inequality of Family Ownership of Labor of Different Grades, 1966

FU 4 MT4 1.00 - FT3 . 0 FT2 * FU3 MT MU4 FUl ~FU2 * MT3 FUI. * MT1 * 'MUl MH4 0 7U FH2 FH3 *M14 .MT2 0 AT LJ*MU2 MU3 0 3 0.50 MH3 o M12 MH2

M13

0 I 5 10 15 20 Wage rate [wi] (thousands of N.T. dollars)

Source: Table 4.13.

-then the number of workers of various grades supplied by families to industry is denoted by Nxi, where i = 1, 2, .. ., 37. Industrial demand, labor supply, and discrimination determine the structure of the wage rates [W] which in turn determines the structure of wage income weights [Ei(:

(4.19) (, .. .., £37) = (WIXI/W, W 2X 2 /W7 .V . , W3 7X37 /W). [see equation (4.16d)] The structure of wage income weights thus reflects demand and supply for various grades of labor for the whole country. The values of 4i are plotted against the wage rate in figure 4.11. These wage income weights measure the contribution of the various grades of labor to the inequality of family wage income, as traced INEQUALITY OF FAMILY WAGE INCOME 179

Figure 4.10. Correlation Characteristics between Total Famiily Incomie and FamnilyOtnership of Labor, 1966

FH2 BH2 FU3. MHS MT4 MU3 1.0 H *FI2 FU2 .: MT2' . M2 MTS Fll ~~FUi M13 FU4M4 * Fll * FT2 *FT3 MU4

* FHI M12 m 0.5 _M14

*MU1 .MH4

FHS- *MT1 C C I I I. 5 *FI3 10 1 5 Wage ao~~~~~~~~~~~aerate ~ ~ [wi]

*-~ (thousands of N.T. dollars) Ml *MHl

*FT1 -0.5 - ML2 *ML4 FL1 MLl .L4 ' FL2 *oFL3 -1.0_

Source: Table 4.13.

to their respective economic importance arising from their large size, high wage, or both. In this sense, workers in the prime age are all economically important, as is seen from the fact that the values of ki are relatively high for them. As a general rule, these workers contribute heavily to inequality. There nevertheless are two exceptions: low-educated males in their prime age (ML2 and ML3). They are economically important because of their large numbers, but they do not contribute heavily to inequality because they are 180 THE INEQUALITY OF FAMILY WAGE INCOME

Figure 4.11. The Economic Weight of Different Grades of Labor, 1966

0.20

MIL2

ML3

Pt¢0. 1 - H

FLI * FL1 . MI2 MHS *MTSH O.1C _

*MU2 0.05 MLI MMUS

MH1 FL3 MI1 F AIML4 FU2 MT2 FUS FII FHI * FH2 TFS U U *FL2S :FIFT1 FT2,FHS MUI AMH4 T41.MU4 0 FL4 5 FIS t1 oTMI4\ 15a 20 FUl MT1 FTS FU4 Wage rate [wi] (thousands of N.T. dollars)

Source: Table 4.13.

mnore evenly distributed among families. As a result, family ownership of highly educated, prime-age workers contributes most to the inequality of family wage income.

Family size and composition The inequality of family wage income is related in part to such economic causes as the demand for, and the supply of, labor having different characteristics, in part to such demographic causes as the INEQUALITY OF FAMILY WAGE INCOME 181 rules governing the formation of families having different membership compositions. Thus the foregoing empirical analysis of the causes of inequality of family wage income merely scratches the surface of complex economic and demographic phenomena. Con- sider some aspects of demographic phenomena. The sex composition of a family is influenced by institutions of monogamous and polyg- amous marriage and by biological laws of reproduction. The age composition of a family is influenced by rules governing the formation of nuclear families, the age at first marriage for males and females, the age at which couples start a new family, and the support of aged parents and grandparents.' 5 The educational composition of a family is influenced by that family's investment in the education of its members. What is needed, then, is a positive theory of family formation that can more satisfactorily explain the inequality of wage income. By positive is meant a theory based on tested and systematized experience, not on speculation. To illustrate the kind of theory required, this discussion concentrates on the educational dimension of the labor force. Note that education is the most important labor characteristic influencing the inequality of family wage income. For each educational attribute the weighted averages of oi, Ri, and Gi (weighted, that is, by sample size) from table 4.13 are plotted against the weighted average of the wage rates [wi] in figures 4.12, 4.13, and 4.14.16 When the educational qualifications of labor increase from primary education, for which the wage rate [wi] was 3.32, to university education, for which the wage rate was 17.5, the distribution of the family ownership of labor becomes more unequal -that is, Gi increases with education in figure 4.12. At the same time, the ownership of high-quality labor is more concentrated in the high wage-income families-that is, Ri increases with education

15. The rules governing the formation of families with respect to sex and age are obviously linked. For example, if a female marries at an earlier age than a male, both the age and sex structure of the family would be affected. More- over different societies have different rules governing the extent to which the young and old establish their own households or stay on as members of the nuclear household. These differences introduce the possibility of bias in all Gini measures. 16. For each variable in table 4.13 the weights are X,/S:, 2`2/8s} ... Xr/:xyX where sr = XI + x2 + . . . + Zr. In words, the weights represent the percentage of the labor force for the various types of labor in each educational category. 182 THE INEQUALITY OF FAMILY WAGE INCOME

Figure 4.12. Weighted Average of the Education Gini plotted against the Average Wage Rate, by Level of Education, 1966

1.00 _ Gini coefficient [Gj] 0.,819 0.75 0.6-549

0.5 - 0.3851

0.25 - 0.1 260

Primary 5 Junior 10 Senior Technical University 20 school high high school (w5 = 17.5) (w, = 3.3) school school (w4 = 14.1) (w2 = 7.6) (w3 = 11.6) Wage rate [wi]

Source: Table 4.13.

Figure 4.13. Weighted Average of the Education Correlation Characteristic Plotted against the Average Wage Rate, by Level of Education, 1966

Correlation characteristic [Ri] 0.9933 1.00 007713 _ A 0.077597 0

0.546 __ 0.25 - 0617 y Primary 5 Junior 10 Senior Technical University 20 school high high school (ws = 17.5) (w, = 3.3) school school (W4 = 14.1) (W2 = 7.6) (w3 = 11.6) Wage rate [wi]

Source: Table 4.13. INEQUALITY OF FAMILY WAGE INCOME 183

Figure 4.14. Weighted Average of the Education Weight Plotted against the Average Wage Rate, by Level of Education, 1966

0.150 0.1432 0.125 - Weight [*i] 0.100 \ 0.075 4 0.050 I 0.0436 0.025F 0.0094I0.005s 0 Primary 5 Junior 10 Senior Technical University 20

school high high school (W5 = 17.5) (w, = 3.3) school school (W 4 = 14.1) (*2 = 7.6) (W3 = 11.6)

Wage rate [wi]

Source: Table 4.13.

in figure 4.13. The pattern of the wage weight [0&] is U-shaped- that is, 4i decreases and then increases with education in figure 4.14. In addition to the issue of how much every term uiRiGi contributes to inequality when the patterns above are empirically given, the theoretical issue is how these patterns are determined in the first place. Families may or may not have different numbers of wage earners. When all families have the same number of workers, the size characteristic is uniform; otherwise it is nonuniform. Simi- larly the educational qualifications of workers in individual families may or may not be the same. When all workers in individual families have the same educational qualifications, the composition characteristic is homogeneous; otherwise it is nonhomogeneous. Four cases will be examined here: uniform size and homogeneous composition; uniform size and semnihomogeneous composition; nonuniform size and homogeneous composition; descending size and homogeneous composition. These four cases indicate the analytical issues in a theory which explains the patterns of ckj, Ri, and Gi in relation to wi for various labor characteristics. 184 THE INEQUALITY OF FAMILY WAGE INCOME

THE UNIFORM-HOMOGENEOUS CASE. It is assumed for the uniform- homogeneous case, the simplest of the four cases, that there are ten families and that every family owns three workers (table 4.14). The first five families own only low-education workers; three families own only medium-education workers; two families own only high-education workers. Thus, of the thirty workers,

Table 4.14. The Inequality of Wage Income: Numerical Example of Uniform Family Size and Homogeneous Family Composition

Family composition (number of members) Medium High Total Low educa- educa- wage Family number and variable education tion tion income

Family 1 3 0 0 60 Family 2 3 0 0 60 Family 3 3 0 0 60 Family 4 3 0 0 60 Family 5 3 0 0 60 Family 6 0 3 0 90 Family 7 0 3 0 90 Family 8 0 3 0 90 Family 9 0 0 3 165 Family 10 0 0 3 165 All families 15 9 6 900

Workers per family [xi] 1.5 0.9 0.6 -

Wage rate [WOi 20 30 55 -

Wage share [0j] 0.333 0.300 0.367 - Gini [Gj] 0.500 0.700 0.800 - Pseudo Gini [0G] -0.500 0.300 0.800 - Correlation characteristic [Ri] -1.000 0.429 1.000 - Wage Gini [G.] - - - 0.217a

- Not applicable. Source: Constructed by the authors. a. G7D= otAzG + lO.R-G.G+ 4ehRhGh = 0.333 X -1.000 X 0.500 + 0.300 X 0.429 X 0.700 + 0.367 X 1.000 X 0.800. INEQUALITY OF FAMILY WAGE INCOME 185 fifteen have low education, nine have medium education, and six have high education. The average number of workers [Xi] of the first type per family is 1.5; that of the second type 0.9; that of the third type. 0.6. The proportionality of these numbers reflects industrial demand. For example, the fifteen workers of the first type might be skilled or unskilled workers; the nine workers of the second type might be white-collar workers; the six workers of the third type might be engineers. The pyramiding pattern of the supply of workers having certain educational attributes, given by (x1 > x2 > X3), shows that industry generally absorbs fewer highly educated workers than it absorbs lowly educated workers. The pattern of the wage rate for the three types of workers is ascending: the hypothetical wage rate is $20 for workers with low education, $30 for those with medium education, and $55 for those with high education, that is, (wi < w2 < W3). The pattern of the values of the wage share is U-shaped: q1 is 0.33; 02 is 0.30; Oais 0.37 (see figure 4.17 below). The empirically observed U-shaped pattern of 4i in figure 4.14 reflects the pyramiding pattern of worker numbers and the ascending pattern of the wage rate for higher educational qualifications. After the grade of technical education, the curve turns up because the effect of increasing wages overwhelms the effect of diminishing numbers. This U-shaped pattern of the wage share [:+] over the wage rate for increasing educational qualifications clearly is the result of the economics of industrial demand and supply. The pattern of family ownership of labor essentially is irrelevant. A positive theory of industrial supply and demand therefore underlies the explanation of the pattern of Oi in the sense that they constitute the economic forces determining the diversity of wage rates as well as the numbers of workers receiving different levels of wage income. For the uniform-homogeneouscase the values of the Gini coefficient [Gi] reveal an increasing pattern when plotted against the wage rate for workers having increasing educational qualifications: the hypothetical Gini coefficientis 0.50 for low education, 0.70 for medium education, and 0.80 for high education. This increasing pattern is the result of the pyramiding pattern of the mean number of workers of a particular educational grade per family [xi] and the labor force's uniform size characteristic and homogeneous composition characteristic. Under the assumptions implicit for the uniform- homogeneous case, workers with low education are more equally distributed among families than are workers with high education, simply because more workers are in the low-education category. 186 THE INEQUALITY OF FAMILY WAGE INCOME

The empirically observed pattern of the Gini coefficient [Gi] in figure 4.12 bears this relation out, except for the dip for university education, which will be explained later. To determine the rank correlation characteristic [Ri] for the uniform-homogeneous case, the total wage inconme of families is used. The hypothetical values of Ri in table 4.14 show an increasing pattern: R1 is -1; R2 is 0.43; R3 is 1. This increasing pattern directly results from the ascending pattern of the wage rate for higher educational qualifications and the labor force's uniform size characteristic and homogeneous composition characteristic. Under the assumptions for this case, high-income families own highly educated workers, a situation which leads to a high correlation between total wage income and the pattern of family ownership of labor; low- income families own lowly educated workers, a situation which leads to a low correlation between total wage income and the pattern of family ownership of labor. This conclusion is borne out by the empirically observed pattern of Ri in figure 4.13. The uniform-homogeneous case thus can adequately explain all the observable patterns of the causes of the inequality of total wage income, which causes are summarized in figures 4.12, 4.13, and 4.14. Its real meaning is that the family is insignificant as a unit of labor ownership, as it will always be when the assumptions of the uniform- homogeneous case are satisfied. If family affiliation is completely disregarded and the Gini coefficient is computed for the thirty workers as individuals, the value of Gi becomes 0.217. Such a Gini coefficient measures the inequality of the wage rate and corresponds to the second level of analysis in the earlier sections of this chapter. Observe that this inequality of the wage rate is exactly the same as the inequality of family wage income. This equivalence indicates that a theory of the inequality of the wage rate is tantamount to a theory of the inequality of family wage income. Thus, for the education characteristic, the theory of the inequality of family wage income is almost completely economic and only slightly demographic: that is, the impact of education on family wage income is deter- rnined by the forces of labor supply, industrial demand, and institutional discrimination, not by the forces of family formation.

THE UNIFORM-SEMIHOMOGENEOUS CASE. For the uniform-semihomogeneous case it is assumed that all families have the same number of workers. With respect to the composition characteristic, however, the behavioristic hypothesis is that the family unit exerts INEQUALITY OF FAMILY WAGE INCOME 187

Table 4.15. The Inequality of Wage Income: Numerical Example of Uniform Family Size and Semihomogeneous Family Composition

Family composition (numberof members) Medium High Total Low educa- educa- wage Family number and variable education tion tion income

Family 1 3 0 0 60 Family 2 3 0 0 60 Family 3 3 0 0 60 Family 4 2 1 0 70 Family 5 2 1 0 70 Family 6 1 2 0 80 Family 7 1 2 0 80 Family 8 0 2 1 115 Family 9 0 1 2 140 Family 10 0 0 3 165 All families 15 9 6 900

Workers per family [xi] 1.5 0.9 0.6 -

Wage rate [Wil 20 30 55 -

Wage share [0i] 0.333 0.300 0.367 - Gini [Gi] 0.447 0.500 0.767 - Pseudo Gini [Gi] -0.447 0.233 0.767 - Correlation characteristic [Ri] -1.000 0.466 1.000 - Wage Gini [G.] - - - 0.202a

- Not applicable. Source: Constructed by the authors. a. G. = kiRiG,+ (mR,.G. + OhRhGh = 0.333 X -1.000 X 0.447 + 0.300 X 0.466 X 0.500 + 0.367 X 1.000 X 0.767.

pressure on all its members to acquire about the same level of education (table 4.15). The homogeneous case manifests the extreme form of such pressure. Here that pressure is more mild, and the education of family members is restricted to adjacent levels of attainment. Because the total number of workers for each level of attainment is the same as in the previous case, the values of the 188 THE INEQUALITY OF FAMILY WAGE INCOME

Figure 4.15. Gini Coefficients in Four Cases Plotted against the Wage Rate, by Level of Education

r .00 ANonuntform homogeneouscase Uniform homogeneouscase

0.75 -___

a0 7'k 0.50 Descending homogeneouscase 0.25 Unform semihomogeneouscase

w, = 20 W2 = 30 Ws = 55 (L) (M) (H) Wage rate [wi] Sources: Tables 4.14-4.17. wage share [E] are unchanged. The economic aspect for the determination of 4i therefore is the same in both cases. The Gini coefficient and the correlation characteristic maintain the same increasing pattern in the uniform-semihomogeneous case as in the uniform-homogeneous case. The values for these variables are plotted against the wage rate in figures 4.15 and 4.16. Note in these figures that the only apparent impact of the semihomogeneous case is to make the distribution of workers more equal for each educational category-that is, for every category Gi is lower in this case than in the homogeneous case. Thus the uniform-semihomogeneous case probably provides a better explanation of the empirical reality observable in the patterns of figures 4.12, 4.13, and 4.14. What then produces that decline in the Gini coefficient for workers with university education in figure 4.12? The Taiwanese greatly value a university education. Moreover, the policy of government for higher education enables persons from all classes of society to obtain a university degree. As a result, workers with a university education tend to be more equally distributed among families than workers with technical education. INEQUALITY OF FAMILY WAGE INCOME 189

Figure 4.16. Correlation Characteristics in Four Cases Plotted against the Wage Rate, by Level of Education

Uniform homogeneouscase m1.00 Uniform semihomogeneouscase \ - 0.75 -

.4 0U.b- ; Nonuniformhomogeneous case

0.25 w,= 20 I

W2 =30 W3 55 -0.25 - T (M) (H)

<-0.50 //4sX Wage rate [wi] o-0.75 \ C) -0.75Descending homogeneous case - 1.00

Sources: Tables 4.14-4.17.

Figure 4.17. Weights in Four Cases Plotted against the Wage Rate, by Level of Education

0.40 - All cases

''0.30 - A f 0.20 be 0.10

W w1 ==20 W2 =30 3 55 (L) (M) (H) Wage rate [wi]

Sources: Tables 4.14-4.17. 190 THE INEQUALITY OF FAMILY WAGE INCOME

THE NONUNIFORM-HOMOGENEOUS CASE. For the nonuniformhomogeneous case it is assumed that the number of workers is different for families, but that the educational qualifications of all workers in a family are the same. Once again, the values of 'i are unchanged so that the other aspects of differences between this case and the uniform-homogeneous case can be concentrated on. What differs is that total family wage income no longer is in a monotonically increasing order (table 4.16). The reason for this change is that large families with low-grade workers can earn more wage income than small families with high-grade workers. For each educational category the distribution of workers among families is more unequal than in the two preceding cases (see figure 4.15). What also differs is that the pattern of the correlation characteristic [Ri] significantly changes: for the low-education category Ri is higher than in the preceding cases; for the high-education category it is lower (see figure 4.16). As with the uniform-semihomogeneous case, the nonuniform-homogeneous case is a more realistic explanation of the observed patterns in figures 4.12-4.14 than is the uniform- homogeneous case.

THE DESCENDING-HOMOGENEOUS CASE. For the descending-homogeneous case it is assumed that the educational qualifications for all workers in a family are the same, but that the number of workers differs in accord with the impact of a new behavioristic hypothesis: families with low-grade workers tend to be larger than those with high-grade workers. Under this assumption the ranking of families by total wage income is completely reversed (table 4.17). Both the Gini coefficient [Gi] and the correlation characteristic ERi] decline as the educational level of workers increases. The observed empirical reality of figures 4.12 and 4.13 contradicts these patterns. Yet, in figure 4.13, Ri is positive for even the lowest level of education-a fact that is inconsistent with the assumptions of the first three cases. This evidence suggests that the behavioristic hypothesis of this case must, at best, be operating mildly. It may thus be concluded that the economic model of the uniform-homogeneous case provides the main explanatory framework for empirical reality and that the demographic forces of family formation of the other cases can only serve to moderate this basic pattern. The similarity of patterns in the numerical examples and the INEQUALITY OF FAMILY WAGE INCOME 191

Table 4.16. The Inequality of Wage Income: Two Numerical Examples of Nonuniform Family Size and Homogeneous Family Composition

Family composition (number of members)

Low Medium High Total education education education wage income

Family number Exam- Exam- Exam- Exam- Exam- Exam- Exam- Exam- and variable ple 1 ple 2 ple 1 ple 2 ple I ple 2 ple I ple 2

Family I 1 1 0 0 0 0 20 20 Family 2 2 2 0 0 0 0 40 40 Family 3 3 3 0 0 0 0 60 60 Family 4 4 0 0 2 0 0 80 60 Family 5 5 4 0 0 0 0 100 80 Family 6 0 0 2 3 0 0 60 90 Family 7 0 5 3 0 0 0 90 100 Family 8 0 0 4 0 0 2 120 110 Family 9 0 0 0 4 2 0 110 120 Family 10 0 0 0 0 4 4 120 220 All families 15 15 9 9 6 6 900 900

Workers per family [si] 1.5 0.9 0.6 -

Wage rate [Wi] 20 30 55 -

Wage share [W] 0.333 0.300 0.367 - Gini [Gi 0.633 0.744 0.833 - Pseudo Gini [Gj] -0.180 0.278 0.767 - Correlation characteristic [Ri] -0.284 0.374 0.921 - Wage Gini [G.] - - - 0.304a

- Not applicable. Source: Constructed by the authors. a. G=RIG,= + 4urnRm.G+ 4hRhGh = 0.333 X -0.284 X 0.633 + 0.300 X 0.374 X 0.744 + 0.367 X 0.921 X 0.833. observed evidence does not imply that the examples explain the evidence. A more rigorous explanation requires an abstract formulation of the ideas embedded in the numerical examples. The effort here has been restricted to pointing out the kind of behav- 192 THE INEQUALITY OF FAMILY WAGE INCOME

Table 4.17. The Inequality of Wage Income: Two Numerical Examples of Descending Family Size and Homogeneous Family Composition

Family composition (numberof members)

Low Medium High Total education education education wage income Family number Exam- Exam- Exam- Exam- Exam- Exam- Exam- Exam- and variable ple I ple 2 ple I ple 2 ple 1 ple 2 ple I ple 2

Family 1 5 0 0 0 0 1.5 100.0 82.5 Family 2 5 0 0 0 0 1.5 100.0 82.5 Family 3 5 0 0 0 0 1.5 100.0 82.5 Family 4 0 0 3 0 0 1.5 90.0 82.5 Family 5 0 0 3 3 0 0 90.0 90.0 Family 6 0 0 3 3 0 0 90.0 90.0 Family 7 0 0 0 3 1.5 0 82.5 90.0 Family 8 0 5 0 0 1.5 0 82.5 100.0 Family 9 0 5 0 0 1.5 0 82.5 100.0 Family 10 0 5 0 0 1.5 0 82.5 100.0 All families 15 15 9 9 6.0 6.0

Workers per family [x,] 1.5 0.9 0.6 - Wage rate [Wi] 20 30 55 Wage share [fi] 0.333 0.300 0.367 - Gini [Gj] 0.700 0.600 0.600 - Pseudo Gini [0G] 0.700 0.100 -0.600 - Correlation characteristic [Ri] 1.000 0.143 -1.000 - Wage Gini [G.] - - - 0.043,

- Not applicable. Source: Constructed by the authors. a. G. = nRzGi+ mRmGm + O6hR)Gh = 0.333 X 1.000 X 0.700 + 0.300 x 0.143 X 0.700 + 0.367 X -1.000 X 0.600.

ioristic hypotheses that need to be made and tested about the rules of family formation if future analysis of the inequality of family wage income is to be improved. DATA ON THE DISTRIBUTION OF FAMILY INCOME 193

Conclusion

In this chapter an attempt has been made to demonstrate that the analysis of the inequality of wage income can be traced to the nonhomogeneity of the labor force and the membership composition of families. The complexity of the problem required a multidimensional cross-listing of data. It also required the conceptual separation of inequality into several levels: the inequality of wage rates, individual wage income, and family wage income. It further required the design of a special analytical framework that combined the regression technique with the additive factor-components technique to process the data at each level. Finally, it required the formulation of new behavioristic hypotheses in areas tangential to traditional economic analysis, such as demography and sociology. At the pretheoretical stage which characterizes this work to date, much effort has gone into the measurement of inequality as an inductive device to examine empirical evidence, rather than into deductive reasoning. This effort should, in turn, help to identify pertinent behavioristic hypotheses which will be needed to determine the inequality of income distribution in the theoretical context of a formal model. Here, only a modest beginning has been made in the formulation of an analytical framework that incorporates the techniques of data generation and processing and the rudiments of theoretical ideas and hypotheses. Clearly, much work remains to be done.

Appendix 4.1. Data on the Distribution of Family Income in Taiwan

By standards of developing countries, statistical data on the distribution of family income in Taiwan is quite satisfactory. Since 1964 there has been a major effort to collect such data on a large scale. This effort has led to the annual publication of reports on the survey of family income and expenditure-reports which constitute the main source of published data.17 This data, collected by the

17. DGBAS, Report on the Survey of Family Income and Expenditure. 194 THE INEQIUALITY OF FAMILY WAGE INCOME

Directorate-General of Budget, Accounting, and Statistics since 1964, will be collectively referred to as DGBAS data. In 1970 the collection of data for the municipality of Taipei became the responsi- bility of the Bureau of Budget and Statistics of the municipal government of Taipei.

Primary data

The DGBAS data is based on information contained in the primary questionnaires (schedules 4.1-4.4). These elaborate questionnaires consist of some 750 questions set up in 750 cells and are to be filled in for every family interviewed. The questions cover such topics as composition of household population, general status of family equipment, current family income, current family expenditure, family capital income and expenditure, agricultural capital income and expenditure, and a detailed breakdown of family consumption expenditure. The sample size-that is, the number of families interviewed-and the sample size as a fraction of the population appear for various years in table 4.18. The number of families interviewed was 3,000 in 1964; it increased to about 6,000 by 1973. Based on the processing of the primary questionnaires, a typical DGBAS annual report contains about 700 pages of tables. The information in these tables provides a much broader coverage than is necessary for most studies of the distribution of family income.

Table 4.18. Size of Sample for DGBAS Surveys, 1964-73

Percentage of Year Families population

1964 3,000 0.146 1966 3,000 0.132 1968 3,000 0.126 1970 3,600 0.160 1972 5,730 0.204 1973 5,790 0.202

Sources: DGBAS, Report on the Survey of Family Income and Expenditure, various years. Schedule 4.1 Record of Family Interview on Income and Expenditure, Page One, 1966

Stratum Cluster |Household A f th Occupation f the Number Con- OO* flu. no* no.i|o.|incom~Ae o.fncomeof ha of the~ch head Sehhead of Huehl of ns mptio Savings househlb oold ld household PoPulaton esn xed b. seb Id~ ~ mplye itnec

Name of Hsien Hsiang Vill ge .in Household household head Address_ Town _ Li City Road _ Section_ .AlDey T..Lne_No._ Distric.t RStreet_ Occupation essential second Amount of

e o 3f 2t i n N h h asinineort is S a ~ ~ Sx -

o ;; , s -4 2 ment he holds ment he holds expendi- income .:: S

- ~~~~~oo_ i ~~~~~~f~Theilol .itiLi

r:.g;]| S[ 2 ] ; 1 ~~~~~~~~~et'abih- x 5,_ F_ iti_ _ I I I I I

Day BadrNumber | Monthly cost| Relatianship Lodger boarder Bore ofrs onh Annual of free meals| } to the | ~~~~~~pendingcharge charge f for relstives,|Rsa} Sexseod adult amoont amount workers, and SexAgeSex Age Sex Age ment Bervants

| fW|_|_|_|_|_|_l co,es-totl nd susac s Domestic|- - | | | | t servants l- - - -Day -Lg Boa- , Number Monthly cost

= Ruainens.- ding e a e-_-e-_R_ark employcesD - -|=|=|=|=|=

1 Farm employees -I-I_I_I_I_1 -1 1 1-

.9 Relatives ______I______I_ _

S.arce: msa-, Reporl on the Srreey of Family Ixcome and Bope-dilore, 1966.

195 Schedule 4.2. Record of Family Interview on Income and Expenditure, Page Two, 1966

Electrical Television sets: Electric fans: Radio: Air conditio.ers: erluipsema H-Roushold - -W" -m HEi equipmehn reorigerat: Pick-up: Electric cooker: Washn

appliance __ _ _ Ice__ box:_ _ _ __ Sewing machines: Camera: T n aest -soe Transport t.bc" Oequi E pment Motor bicycle: Bicycles: Pedicab: Sedan: Cultural uuage | Newspaper: Magazine: Income amount Name Kinds Periodical income oa of and - - T Otker Amount retained Amount for > income ofu Total Monthly (including for personal use ily consumption =_ maker incoe or Annual temporary _ 8CO quartsrly income)

EiX

A ~~~~~~~~~~Amountyearly .= El ItemYtiemrenY |nkCi°ndm1o°f each 1 income Item | Injome Yearly of each income I time,total ~~~~kindtimes ltime totsl n e ~~~~~~~~~~~~~~~Interest Net | -_- _ Ei operating Investment m.Icome___ Tranafers from § ______hounehold ._ Net proton- Transfers from sional2 income government Net T~~~~~~~~~~reansferofrmm agriculturalc agncNueltural l | | Transfersenterprise from | 1 I V ______l abroad RRent Others _ _ , ~~~~~~~~~~~~~~~~~~Expenditure l amount Item Illustrations of various items Monthly Yea Remarks | quarterly total

Total I I

_Riee l (omitted) a FFloure s Sweetpotato ______O ) e l | Other cereals -n Subsidiary food MIlklo w Condiment Eating out -- l ;Dinners for festivals Marriages, births, birthdays, to ( funerals, and feasts

|4|Noaleoh oli l

ANlcoholic

S Tobacco

Scoree: Same as for schedule 4.1.

196 Schedule 4.3. Record of Family Interview on Income and Expenditure, Page Three, 1966

_ Expenditure I ~~~~~~~~~amount Flour Item Illustrations of various items MonthlY Remarks

______._ quarterly | ot Total Monetary service | (omitted) r 3 Education and research : Marriages, births, birthdays, .S and funerals aZ Other

c c 8 Interest

c Taxes Total To households To government _ c To enterprwses

3 To abroad Agriculturalproductive expeniditure Flour Item Illustrations of varioss Ateres Total |Pemar}s| Capital Total Drawing from deposits (omitted) E Mutual savingsand capital _ _ _ o o; Loanrepayment ____ Borrowinig ______Salesof land 5 Sales of houses w; Purohases on credit Other capital in^ome El Total Deposits.______- a Payment to mutual aaviugs 8 and msurance

Repayment of loan Purchases of land _ l_ l S Purchases of houses ) Repayment for purchases on credit Other capital expenditure ______

8J_ = $3 1 Agricultural income

Agricultural expenditure

8 Name of the respondent The survey takes--minutes

; The abode belongs to The cooperation of this househ9ld .

Conductor: Enumerator: Survey date:

Source; Same as for sehedule 4.1.

197 Schedule4.4. Record of Family Intervieiv on Incoine and Expenditure, Page Four, 1966

Stratum Cluster, Househod Ageof th, Occ"P&ton~Se- f th, Number Consu- no 0n. no. Income hehasdoOf| ofthe rehead d....hld f iexen'lpern Savigs

Expenditure amount Flour Item Illustrations of -fious items Monthly | Yealy emak quarterly |total TotalI *o Ma.'s clothing (omitted) rQ0 Woman'sclothing -^& Child's clothing °a Jewelry,ornaments, and o miscellaneous T otal =Rent > | Actual c f I~~mputed =o House repairnng and f installation Water ch.,ge Total Eleetticity bill ^= Charcoal Coal = Liquid fuel|

G. faSouel Plant wastes Oth-rl

E a Furniture .d equipment =

a =. Textiles - Appliances for kitchenand _ _ Other = Total o Domesticsenants =o&Other householdoperation o expenres =, Total =c Persnal careml Hair d-essi.gand bath

g E | Medicaland healthexpesaes lTotalll l l e 1Purnhases of pemsnal 8 transport equipment f =,|Operationof persontal 8rnprt x equipment

Sou,-e Sameas for schedule 4.1.

198 DATA ON THE DISTRIBUTION OF FAMILY INCOME 199

Nevertheless the framework underlying the design of these tables is not specifically suited to the analytical study, such as that in this chapter, of causes of the inequality of family income. Consequently we had to return to the primary questionnaires to obtain the cross- listing of information needed for this chapter.

Analytical cross-listing of data For the joint project of Yale's Economic Growth Center and Taiwan's Economic Planning Council, the cross-listing of data is given by the coded family-income data form-to be referred to as the coded form (schedule 4.5). There are fifty-one cells in this form. From the information contained in the primary questionnaires of the DGBAS data, all cells are filled in for every family; every family has one card. These coded forms are preserved in cards (for 1966 in computer cards) for almost all 24,120 families covered in table 4.18. The coded form contains two basic types of information: wage and nonwage income. There are three kinds of nonwage income: property income from interest, rent, and investment; mixed income from agricultural, business, and professional activities; and transfer income. Mixed income is a mixture of wage and property income. It occurs primarily because the family and the production unit coincide-for example, a family-operated farm, a family business, or a dentist's office-making it impossible to separate the wage and property components of income paid by the production unit to the family. Transfer income consists of government transfer or welfare payments; it accounts for less than 1 percent of total family income. The coded form contains the following information on wage income for every wage earner: sex, age, education, occupation, job location, number of wage earners, and total income earned by each wage earner. Total family income (for example, NT$53,647 in schedule 4.5) is the sum of total wage income (NT$23,800), total property income (NT$3,600), total mixed income (NT$26,247), and transfer income (0). The coded form also contains information on family location, family type, and the year surveyed. For this chapter, use was not made of the information on nonwage income, but all information relevant to the analysis of wage income was coded (table 4.19). Five characteristics are indicated in that table for individual wage earners and two characteristics for every wage-earning family. Each characteristic may be thought of as a 200 THE INEQUALITY OF FAM1ILY WAGE INCOME

Table 4.19. Coding for Characteristics of Individual Wage Earners and Income-earning Families

Value of characteristic

Characteristic 2 3

Individual wage earners Sex Female Male Age Under 25 25-45 45-60 Education Primary school Junior high Senior high (six years) school (nine school (twelve years) years) Occupation Public employee Specialist or pro- Service employee or serviceman fessional Job location Rural village Township City

Income-earning families Family type Farm Nonfarm

Value of characteristic Family location 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 County

- Not applicable. Source: Constructedby the authors. variable that takes on one of a finite number of values. The sex variable can be coded either as female (1) or male (2). The age variable assumes one of four possible values: under 25 (1), 25-45 (2), 45-60 (3), or over 60 (4). The education variable takes on one of five values corresponding to the gradation of the formal education system: primary school (1), junior high school (2), senior high school (3), technical school (4), or university (5). Intuitively the characteristics just mentioned are most significant among the various factors relevant to the analysis of wage income inequality. DATA ON THE DISTRIBUTION OF FAMILY INCOME 201

Value of characteristic

4 6 6 Characteristic

Individual wage earners

- - - Sex

Over 60 - Age

Technical school University (six- - Education (fourteen years) teen years)

Commercial self- Manual laborer Agricultural Occupation employee employee

- - Job location

Income-earning families Family type Value of characteristic 17 18 19 20 21 Family location Municipality

The occupation variable has six values: government employee and serviceman (1), specialist or professional (2), service employee of business establishments (3), commercial self-employee (4), manual laborer (5), and agricultural employee (6). The classification of labor according to this criterion corresponds to the homogeneous groups within a "working class." The variable for job location has three values: rural village (1), township (2), and city (3). The variable for "family type" classifies a family as a farm (1) or nonfarm (2) family. The definition of farm family adopted by the DGBAS is based on one of five possible criteria of agricultural activi- 202 THE INEQUALITY OF FAMILY WAGE INCOME

Schedule 4.5. Coded Form for Data on Family Income, with Sample Entries

Year FamilyFamily Total Total Total Transfer Total Year lation type wage property mixed income family income income income income

1973 01 2 23,800 3,600 26,247 0 53,647

Wage income

Wage earner 1 2 3 4 5 6

Wage income 9,600 1,000 7,200 6,000

Sex 1 1 1 1

Age 1 1 3 1

Education 2 1 1 1

Occupation 3 6 6 6

Job location 1 1 1 1

Nonwage income

Property income Mixed income

Intersticome Rent Invest- Agricul- Business Profes- Transfer Interest income income .ment tural income sional income income income income

0 3,600 0 26,247 0 0 0

Note: See table 4.19 for values assigned to characteristics. Source: Constructed by the authors. MODEL OF ADDITIVE FACTOR COMPONENTS 203 ties.18 The "farnily location variable" has twenty-one values corresponding to the administrative districts of Taiwan.' 9 Thus, in the coded forms (schedule 4.5), individual wage income earners are coded according to the five "individual wage earner's characteristics" of table 4.19. At the same time, families are coded according to the two "family characteristics" of that table. The cross-listing of the data in this way constitutes the primary input of our analysis of wage income inequality (tables 4.20-4.27). It should be apparent that the identification of these characteristics is essentially guided by an intuitive notion of what is relevant to the analysis of wage income inequality.

Appendix 4.2. Linear Regression and the Model of Additive Factor Components

The method we have designed for the analysis of wage income inequality is built on a combination of the technique of linear regression and the technique of additive factor components. For expository convenience the analytical design has been presented in chapter four with the aid of numerical examples. The two techniques can also be stated abstractly-that is, independent of their empirical applications. The linear regression technique can be stated as follows:

(4.20) y = ao + aix, + a2X2 + . .. ±+ arxr, where y is regressed on r explanatory variables [xi]. If there are n empirical observations, this gives:

(4.21) (Yiy Xil, Xi2) ... Zir)X(i)= 1 2,. .. , n) With the aid of expression (4.21) the regression coefficients aj (j = 0, 1, 2,..., r) can be estimated. The data input required for

18. These criteria are cultivating an area of 0.2 hectares, raising more than three pigs of not less than sixty kilograms each, raising more than one buffalo, raising more than one hundred poultry, and yearly sales of agricultural products of more than NT$6,000. A "fishing family" is similarly defined by the number of fish-catching and fish-growing activities. 19. The twenty-one districts comprise sixteen counties-Taipei, Ilan, Taoyuan, Hsinchu, Miaoli, Taichung, Changhwa, Nantou, Yunlin, Chiayi, Tainan, Kaoh- siung, Pingtung, Taitung, Hwalien, and Penghu-and five municipalities- Keelung, Taichung, Tainan, Kaohsiung, and Taipei. 204 THE INEQUALITY OF FAMILY WAGE INCOME

Table 4.20. Annual Wage Rates of Female Workers, by Age, Occupation, Job Location, and Level of Education, 1966 (N.T. dollars) Under25 years 25-45 years Level of education Rural Rural and occupation area Town City area Town City

Primary school Public employee - 6,160 9,533 4,950 60,300 7,500 Specialista - - 2,568 - - - Service employeeb 4,050 6,363 4,746 7,008 7,180 6,186 Commercial self-employee - - 8,200 16,640 4,400 18,400 Manual laborer 5,015 5,859 6,265 4,035 5,796 8,180 Agricultural employee 2,502 1,630 9,600 2,602 3,035 11,400 Junior high school Public employee - 13,060 10,620 12,540 20,500 12,100 Specialist 4,800 7,000 - - - - Service employee - 5,850 7,800 - 8,400 - Commercialself-employee - 3,500 - 0 11,650 - Manual laborer 5,820 7,115 8,150 - 5,676 - Agricultural employee 6,000 - - 3,200 7,800 - Senior high school Public employee 12,922 10,196 11,010 8,566 16,076 20,413 Specialist - - - - - Service employee ------Commercial self-employee - 7,470 16,710 - - 23,375 Manual laborer - - - - 5,300 - Agricultural employee ------Technicalschool Public employee - - 20,500 - - 20,866 Specialist ------Service employee - - 12,000 - - - Commercial self-employee - - - - - 21,400 Manual laborer - - - - - Agricultural employee ------Universityor over Public employee 17,908 - - - 10,050 - Specialist ------Service employee ------Commercialself-employee - - - - - 43,200 Manual laborer ------Agricultural employee ------

- No entry. Source:DGBAs, Reporton the Surveyof Family Incomeand Expenditure,1966. MODEL OF ADDITIVE FACTOR COMPONENTS 205

45-60 years Over 60 years

Rural Rural Level of education area Town City area Town City and occupation

Primary school - 12,222 3,900 - - - Public employee - - - - - Specialist, - 5,100 6,685 2,700 4,332 - Service employeeb ------Commercial self-employee 8,550 5,783 5,600 - - 7,800 Manual laborer 2,894 3,580 - 2,800 - - Agricultural employee Junior high school 13,661 - - - - - Public employee ------Specialist - 9,900 - - - - Service employee - - - - - Commercial self-employee ------Manual laborer ------Agricultural employee Senior high school - 29,703 24,080 - - - Public employee - - - - - Specialist - - - - Service employee - 26,695 33,000 - - - Commercial self-employee - = - - - - Manual laborer ------Agricultural employee Technical school - - - - - Public employee - - - - - Specialist - - - - - Service employee ------Commercial self-employee ------Manual laborer - - - - - Agricultural employee University or over - 1L8,600 - - - - Public employee - 30,000 - - - Specialist ------Service employee ------Commercial self-employee ------Manual laborer ------Agricultural employee

a. Includes professionals. b. Includes servicemen. 206 THE INEQUALITY OF FAMILY WAGE LABOR

Table 4.21. Annual Wage Rates of Male Workers, by Age, Occupation, Job Location, and Level of Education, 1966 (N.T. dollars)

Under 25 years 25-45 years

Level of education Rural Rural and occupation area Town City area Town City

Primary school Public employee 10,590 8,104 15,900 20,721 18,017 17,256 Specialista ------Service employeeb 3,103 5,852 8,871 12,300 14,175 15,627 Commercial self-employee - 7,540 15,000 8,325 3,186 21,287 Manual laborer 9,015 7,573 7,082 12,470 14,365 19,034 Agricultural employee 3,248 3,107 2,250 5,239 5,292 22,900 Junior high school Public employee - 11,736 12,750 19,319 18,487 21,901 Specialist ------Service employee 41,000 7,600 7,600 - 8,840 16,985 Commercial self-employee 6,000 7,750 14,000 - 11,000 28,000 Manual laborer 1,070 9,710 12,033 14,750 1,475 9,540 Agricultural employee 4,500 1,500 4,800 5,200 11,875 - Senior high school Public employee 11,635 10,881 11,160 19,177 22,404 22,404 Specialist - - - - 32,760 - Service employee 1,600 19,200 11,280 9,600 17,935 32,230 Commercial self-employee - 12,000 13,166 19,814 14,711 25,500 Manual laborer - 11,200 12,900 - 12,961 23,133 Agricultural employee - - - 4,200 7,300 - Technicalschool Public employee - - - 21,264 21,230 32,546 Specialist - 4,095 - 46,800 - - Service employee - - - - - Commercial self-employee - 8,100 21,500 - 24,260 - Manual laborer ------Agricultural employee ------University or over Public employee - - 17,400 25,500 27,479 25,584 Specialist - - - - 12,600 - Service employee - - - - - 90,600 Commercial self-employee - - - 12,600 41,500 56,671 Manual laborer ------Agricultural employee - - -

- No entry. Source: Same as for table 4.20. MODEL OF ADDITIVE FACTOR COMPONENTS 207

46-60 years Over 60 years

Rural Rural Level of education area Town City area Town City and occupation

Primary school 16,616 21,803 22,803 11,942 7,959 8,070 Public employee - 7,200 - - - - Specialist, 1,800 8,614 17,722 - - 10,400 Service employeeb 24,045 22,966 30,554 25,184 8,190 16,800 Commercial self-employee 10,161 13,606 19,367 2,600 8,757 12,440 Manual laborer 5,593 5,239 5,931 3,800 5,142 - Agricultural employee Junior high school 23,982 20,585 28,492 - - - Public employee ------Specialist - 12,550 18,650 - - - Service employee 4,000 24,345 36,675 - 29,200 - Commercial self-employee - 16,000 30,300 - - 57,360 Manual laborer 3,000 5,925 - - - - Agricultural employee Senior high school 26,960 22,783 32,054 - 17,975 26,100 Public employee ------Specialist - 3,000 - - - - Service employee - 29,566 16,382 - - 42,200 Commercial self-employee - 14,200 28,953 - - - Manual laborer ------Agricultural employee Technical school - 44,853 32,600 - - - Public employee - - 7,200 19,100 - - Specialist - - - - - Service employee ------Commercial self-employee ------Manual laborer ------Agricultural employee University or over - 33,475 52,226 - - 56,418 Public employee - 16,800 56,610 - - - Specialist - - 37,400 - - - Service employee - 34,150 34,600 - - - Commercial self-employee - - 33,300 - - - Manual laborer ------Agricultural employee

a. Includes professionals. b. Includes servicemen. 208 THE INEQUALITY OF FAMILY WAGE LABOR

Table 4.22. Number of Female Workers, by Age, Occupation, Job Location, and Level of Education, 1966

Under 25 years 25-45 years

Level of education Rural Rural and occupation area Town City area Town City

Primary school Public employee - 2 3 1 1 2 Specialista - - 1 - - - Service employeeb 4 8 15 6 13 20 Commercial self-employee - - 1 1 1 1 Manual laborer 18 45 41 9 30 20 Agricultural employee 82 40 1 100 58 4

Junior high school Public employee - 5 4 2 3 2 Specialist 1 1 - - - - Service employee - 2 3 - 1 - Commercial self-employee - 1 - - 3 - Manual laborer 2 8 4 - 4 - Agricultural employee 1 - - 1 1 -

Senior high school Public employee 32 10 3 31 11 8 Specialist ------Service employee ------Commercial self-employee - 5 4 - - 4 Manual laborer - - - - 3 Agricultural employee - - - - -

Technical school Public employee - - 1 - - 3 Specialist ------Service employee - - 1 - - - Commercial self-employee - - - - - 2 Manual laborer ------Agricultural employee ------MODEL OF ADDITIVE FACTOR COMPONENTS 209

45-60 years Over 60 years

Rural Rural Levelof education area Town City area Town City and occupation

Primary school - 2 1 - - - Public employee ------Specialista - 1 7 1 2 - Service employeeb Commercial - - - - - self-employee 4 11 3 - - 1 Manual laborer 20 10 - 2 - - Agricultural employee

Junior high school 1 ------Public employee ------Specialist - 1 - - - - Service employee Commercial ------self-employee ------Manual laborer ------Agricultural employee

Senior high school - 2 2 - - - Public employee ------Specialist ------Service employee Commercial - 1 2 - - - self-employee - - - - - Manual laborer ------Agricultural employee

Technical school ------Public employee ------Specialist ------Service employee Commercial ------self-employee ------Manual laborer ------Agricultural employee (Table continues on the followingpages) 210 THE INEQUALITY OF FAMILY WAGE INCOME

Table 4.22 (Continued)

Under 25 years 25-45 years Level of education Rural Rural and occupation area Town City area Town City

University or over Public employee 1 - - - 2 Specialist - - Service employee - - - - - 1 Commercial self-employee ------Manual laborer ------Agricultural employee -

- No entry. Source:Same as for table 4.20. a. Includes professionals. b. Includes servicemen. expression (4.21) can be written as column vectors:

(4.22a) Y = col(y1, Y2,..., y,.)

(4.22b) Xi = Col(Xli, X 2V,..., Xi) (i = 1, 2,..., n) With the aid of the estimated regression equation, this gives:

(4.23a) Y = A. + a1X 1 + a 2 X 2 +.. . + a,X, + 0, where

(4.23b) A. = col(a0 , aO,... a) and

(4.23c) 6 = col(Oi,02, ... Xt), and where 6i is the difference between yi and yi, as estimated from regression equation (4.20) for the ith observation. It can now be clearly seen how equation (4.23a) may be viewed as an abstract problem of additive factor components. An application of the general decomposition technique for such a problem immediately leads to:

(4.24) G5 = klR,G(X,)+ 0 2R2 G(X2) +. . . + 4r,RG(Xr) + OeReG(0), where ci is the share, Ri the correlation characteristic, and G(Xi) the MODEL OF ADDITIVE FACTOR COMPONENTS 211

45-60 years Over 60 years

Rural Rural Level of education area Town City area Town City and occupation

University or over - 1 - - - - Public employee - - 1 - - - Specialist ------Service employee Commercial ------self-employee ------Manual laborer ------Agricultural employee

Gini coefficient of Xi. The causation of G, can thus be traced to the various quality dimensions emphasized in the regression equation.2 0 The methodological innovation of this chapter thus resides in the combination of the linear regression technique with the additive factor-components technique. For this combination to work, the additive property of the Gini coefficient is essential-that is, it underlies equation (4.24). Moreover the additive property of the linear regression equation (4.20) is equally essential. For example, in the earnings equation in chapter four, the wage rate is assumed to be additively determined and traced to various dimensions of the quality of the labor force. The linearity of the regression is not essential for the combination of the two techniques. The combination still is possible when the regression equation is nonlinear, and this possibility indicates a direction in which the method can be generalized.

20. Because of the technical complexities, full treatment of the decomposition analysis for the problem of additive factor components is postponed to part two. Notice, however, that the term associated with OeRoG(6) in equation (4.24) arises from the error term [9] in equation (4.23a). To the extent that the error term is small-that is, to the extent that the multiple linear correlation in the regression analysis of equation (4.21) is high-the influence of this term in equation (4.24) similarly is small. One proviso is intuitively obvious: to the extent that the regression analysis is imperfect, we cannot hope to explain inequality fully. 212 THE INEQUALITY OF FAMILY WAGE INCOME

Table 4.23. Number of Male Workers, by Age, Occupation, Job Location, and Level of Education, 1966

Under 26 years 26-46 years

Level of education Rural Rural and occupation area Town City area Town City

Primary school Public employee 3 9 2 13 60 32 Specialista I - - - - - Service employeeb 4 9 7 5 17 20 Commercial self-employee - 1 2 2 9 18 Manual laborer 19 50 72 46 121 112 Agricultural employee 74 43 4 202 154 3

Junior high school Public employee - 5 2 7 28 19 Specialist ------Service employee 2 2 1 - 3 7 Commercial self-employee 1 2 1 - 2 4 Manual laborer 1 13 3 4 10 10 Agricultural employee 3 2 1 7 4 -

Senior high school Public employee 4 4 1 13 66 34 Specialist - - - - 1 - Service employee 1 1 1 1 7 3 Commercial self-employee - 1 6 8 17 16 Manual laborer 2 2 - 6 9 Agricultural employee - - - 2 2 -

Technical school Public employee - - - 2 7 10 Specialist - 1 - 1 - - Service employee ------Commercial self-employee - 1 1 - 1 - Manual laborer ------Agricultural employee ------MODEL OF ADDITIVE FACTOR COMPONENTS 213

46-60 years Over 60 years

Rural Rural Levelof education area Town City area Town City and occupation

Primary school 10 23 23 2 4 3 Public employee ------Specialist" 1 7 9 - - 1 Service employeeb Commercial 2 3 7 1 1 2 self-employee 10 51 43 2 8 5 Manual laborer 63 54 6 3 12 - Agricultural employee

Junior high school 2 12 9 - - - Public employee ------Specialist - 2 2 - - - Service employee Commercial 1 1 3 - 1 - self-employee - 1 2 - - - Manual laborer 1 2 - - - - Agricultural employee

Senior high school 6 35 20 - 2 1 Public employee ------Specialist - 1 - - - - Service employee Commercial :-: 3 4 - - 1 self-employee - 1 3 - - - Manual laborer ------Agricultural employee

Technical school - 3 1 - - - Public employee - 1 1 - - Specialist ------Service employee Commercial ------self-employee ------Manual laborer ------Agricultural employee (Tablecontinues on thefollowing pages) 214 THE INEQUALITY OF FAMILY WAGE INCOME

Table 4.23 (Continued)

Under 25 years 25-45 years

Level of education Rural Rural and occupation area Town City area Town City

University or over Public employee - - 1 2 23 19 Specialist - - - - 1 Service employee - - - - - 2 Commercial self-emplovee - - - 1 4 7 Manual laborer ------Agricultural employee -

- No entry. Source:Same as for table 4.20. a. Includes professionals. b. Includes servicemen.

When abstractly stated, the method can be applied to other problems as well-for example, to the analysis of the inequality of the distribution of family property income [GJ. The total family property income [y] can, as in equation (4.20), first be regressed on a number of explanatory variables [xi] representing particular types of assets, such as urban land, physical capital, and bonds, or the "class" affiliation of the family, such as that of the entrepreneurial class, the professional class, or the class of skilled workers. The regression results can then be combined with the model of additive factor components to trace the inequality of family property income to the unequal distribution of the ownership of assets, to the class affiliation of families, or to both. The crude earnings function used in chapter four obviously does injustice to an approach which has received a good deal of professional attention of late.2 ' In this chapter we have somewhat downgraded the

21. Among the shortcomingsof the earnings function used in chapter four, the followingmay be mentioned: the ambiguityof age as a proxy for experience; the inadequacy of total familyincome as a proxy for familyinfluence; the interpretation of G6.when x is an ordinal-for example,when education is measured by low, medium,and high, not by years of education; the lack of effort to compare our conclusions,such as those on returnsto education,with other, inde- pendentstudies. MODEL OF ADDITIVE FACTOR COMPONENTS 215

45-60 years Over 60 years

Rural Rural Level of education area Town City area Town City and occupation

University or over - 14 16 - - 3 Public employee - 1 1 - - - Specialist - - 1 - - - Service employee Commercial - 2 1 - - - self-employee - - 1 - - - Manual laborer - - - - - Agricultural employee earnings-function approach. This approach by itself, used for the first level of analysis in our design, really is insufficient for the analysis of income inequality. It becomes significant for such analysis only after it is combined with the model of additive factor components. The argument in this appendix thus suggests that the regression approach can play a significant role in the analysis of income inequality when it is imbedded in a framework involving the model of additive factor components. 216 THE INEQUALITY OF FAMILY WAGE INCOME

Table 4.24. Number of Rural Workers and Average Annual Wage Rate, by Education, Sex, and Age, 1966

Number of workers

Junior Senior Techni- Univer- Primary high high cal sity or Sex and age school school school school over Total

Female 248 8 6 1 263

Under 25 years 104 4 3 - 1 112 25-45 years 117 3 3 - - 123 45-60 years 24 1 - - - 25 Over 60 years 3 - - - - 3

Male 462 29 35 4 3 533 Under 25 years 100 7 5 - - 112 25-45 years 268 18 24 3 3 316 45-60 years 86 4 6 - - 96 Over 60 years 8 - - 1 - 9

Both sexes 710 37 41 4 4 796 Under 25 years 204 11 8 - 1 224 25-45 years 385 21 27 3 3 439 45-60 years 110 5 6 - - 121 Over 60 years 11 - - 1 12

- No entry. Source: Same as for table 4.20. MODEL OF ADDITIVE FACTOR COMPONENTS 217

Annual wagerate

Junior Senior Techni- Univer- Primary high high cal sity or school school school school over Total Sex and age

3,114 8,048 10,745 - 17,908 3,495 Female 2,997 5,610 12,923 - 17,908 3,489 Under 25 years 3,079 9,427 8,567 - - 3,368 25-45 years 3,837 13,661 - - - 4,230 45-60 years 2,767 - - - - 2,767 Over 60 years

6,864 13,385 18,164 27,107 26,367 8,222 Male 4,559 14,653 9,628 - - 5,416 Under 25 years 7,387 12,813 17,742 29,776 26,367 8,875 25-45 years 7,791 13,741 26,961 - - 9,237 45-60 years 8,209 - - 19,100 - 9,419 Over 60 years

5,554 12,731 17,078 27,107 24,252 6,660 Both sexes 3,762 11,365 10,864 - 17,908 4,453 Under 25 years 6,077 12,330 16,723 29,766 26,367 7,332 25-45 years 6,928 13,725 26,961 - - 8,203 45-60 years 6,724 - - 19,100 - 7,756 Over 60 years 218 THE INEQUALITY OF FAMILY WAGE INCOME

Table 4.25. Number of Town Workers and Their Annual Wage Rate, by Education, Sex, and Age, 1966

Number of workers

Junior Senior Techni- Univer- Primary high high cal sity or Sex and age school school school school over Total

Female 224 30 32 - 3 289 Under 25 years 95 17 15 - - 127 25-45 years 103 12 14 - 2 131 45-60 years 24 1 3 - 1 29 Over 60 years 2 - - - - 2

Male 637 90 149 13 45 934 Under 25 years 112 24 8 2 - 146 25-45 years 361 47 99 8 28 543 45-60 years 139 18 40 3 17 217 Over 60 years 25 1 2 - - 28

Both sexes 861 120 181 13 48 1,223 Under 25 years 207 41 23 2 - 273 25-45 years 464 59 113 8 30 674 45-60 years 163 19 43 3 18 226 Over 60 years 27 1 2 - - 30

- No entry. Source:Same as for table 4.20. MODEL OF ADDITIVE FACTOR COMPONENTS 219

Annual wage rate

Junior Senior Techni- Univer- Primary high high cal sity or school school school school over Total Sex and age

4,633 9,636 12,422 - 2,900 6,103 Female 4,127 8,495 9,288 - 5,322 Under 25 years 4,932 11,230 13,767 - 10,050 6,531 25-45 years 5,374 9,900 22,034 - 18,600 7,709 45-60 years 4,333 - - - - 4,333 Over 60 years

9,946 13,339 19,771 24,587 30,320 13,026 Male 5,763 9,109 12,141 6,098 - 6,667 Under 25 years 10,814 13,370 19,288 21,609 28,951 13,675 25-45 years 11,617 18,018 22,583 44,853 32,574 16,270 45-60 years 6,872 29,200 17,975 - - 8,462 Over 60 years

8,564 12,414 18,475 24,857 29,231 11,390 Both sexes 5,012 8,855 10,280 6,098 - 6,041 Under 25 years 9,508 12,935 18,604 21,609 27,691 12,286 25-45 years 10,698 17,591 22,544 44,853 31,797 16,612 45-60 years 6,684 29,200 17,975 - - 8,187 Over 60 years 220 THE INEQUALITY OF FAMILY WAGE INCOME

Table 4.26. Number of City Workers and Their Annual Wage Rate, by Education, Sex, and Age, 1966

Number of workers

Junior Senior Techni- Univer- Primary high high cal sity or Sex and age school school school school over Total

Female 121 13 23 7 2 166 Under 25 years 62 11 7 2 - 82 25-45 years 47 2 12 5 1 67 45-60 years 11 - 4 - 1 16 Over 60 years 1 - - - - 1

Male 361 65 101 13 52 592 Under 25 years 87 8 10 1 1 107 25-45 years 175 40 62 10 28 315 45-60 years 88 16 27 2 20 153 Over 60 years 11 1 2 - 3 17

Both sexes 482 78 124 20 54 758 Under 25 years 149 19 17 3 1 189 25-45 years 222 42 74 15 29 382 54-60 years 99 16 31 2 21 169 Over 60 years 12 1 2 - 3 18

- No entry. Source: Same as for table 4.20. MODEL OF ADDITIVE FACTOR COMPONENTS 221

Annual wage rate

Junior Senior Techni- Univer- Primary high high cal sity or school school school school over Total Sex and age

6,766 12,772 20,471 19,700 36,600 10,040 Female

6,081 8,953 14,267 16,250 - 7,413 Under 25 years 7,794 33,780 21,401 21,080 43,200 12,527 25-45 years 6,136 - 28,540 - 30,000 13,229 45-60 years 7,800 - - - - 7,800 Over 60 years

15,998 37,725 24,393 29,751 43,998 22,577 Male 7,389 11,000 12,724 21,500 17,400 8,383 Under 25 years 18,489 46,061 23,784 32,547 38,000 25,213 25-45 years 20,071 29,022 29,388 19,900 51,862 26,805 45-60 years 11,856 57,360 34,150 - 56,419 25,019 Over 60 years

13,680 33,566 23,665 26,233 43,724 19,831 Both sexes 6,845 9,815 13,360 18,000 17,400 7,962 Under 25 years 16,225 45,476 23,398 28,724 38,180 22,988 25-45 years 18,523 29,022 29,279 19,900 50,821 25,519 45-60 years 11,518 57,360 34,150 - 56,419 24,063 Over 60 years 222 TIHE INEQUALITY OF FAMILY WAGE INCOME

Table 4.27. Number of Workers and Average Annual Wage Rate, by Education, Sex, and Age, 1966

Number of workers

Junior Senior Techni- Univer- Primary high high cal sity or Sex and age school school school school over Total

Female 593 51 61 7 6 718 Under 25 years 261 32 25 2 1 321 25-45 years 267 17 29 5 3 321 45-60 years 59 2 7 - 2 70 Over 60 years 6 - - - - 6 Male 1,460 184 285 30 100 2,059 Under 25 years 299 39 23 3 1 365 25-45 years 804 105 185 21 59 1,174 45-60 years 313 38 73 5 37 466 Over 60 years 44 2 4 1 3 54 Both sexes 2,053 235 346 37 106 2,777 Under 25 years 560 71 48 5 2 686 25-45 years 1,071 122 214 26 62 1,495 45-60 years 372 40 80 5 39 536 Over 60 years 50 2 4 1 3 60

- No entry. Source: Same as for table 4.20. MODEL OF ADDITIVE FACTOR COMPONENTS 22

Annual wage rate

Junior Senior Techni- Univer- Primary high high cal sity or school school school school over Total Sex and age

4,433 10,186 15,303 19,700 21,635 6,058 Female 4,141 8,292 11,118 16,250 17,908 5,217 Under 25 years 4,624 13,564 16,388 21,080 21,100 6,570 25-45 years 4,891 11,781 25,752 - 24,300 7,728 45-60 years 4,128 - - - - 4,128 Over 60 years

10,647 21,961 21,211 27,161 37,314 14,529 Male 5,833 10,492 11,848 11,232 17,400 6,786 Under 25 years 11,342 25,728 20,594 27,984 33,114 15,479 25-45 years 12,943 22,201 25,460 34,872 43,000 18,280 45-60 years 8,361 43,280 26,063 19,100 56,419 13,834 Over 60 years

8,724 19,406 20,201 25,749 36,426 12,388 Both sexes 5,045 9,500 11,468 13,239 17,654 6,052 Under 25 years 9,667 24,033 20,024 26,656 32,533 13,566 25-45 years 11,666 21,680 25,485 34,872 19,100 25,749 45-60 years 7,853 43,280 26,063 19,100 56,419 12,863 Over 60 years CHAPTER 5

Income Distribution and EconomicStructure

THE CAUSES OF THE INEQUALITY of family income were explicitly traced in earlier chapters to additive factor-income components. In this chapter a more aggregate view is taken by deemphasizing additive factor components and concentrating on the structure of total family income. This aggregate view facilitates tracing the inequality of family income to various homogeneous categories of income recipients. Such analysis is hardly revolutionary. Kuznets's classical study, inquiring whether inequality in the distribution of family income increases in the course of industrialization and urbanization, emphasized sectoral and locational dimensions.' Sub- sequent studies by other investigators have done the same. In this chapter, too, sectoral and locational dimensions constitute the two focal points of an analysis that will be formulated as an abstract model of homogeneous groups. As part of this analysis, the inequality of family income will be examined in relation to family attributes. The income gaps between families in different sectors and locations are an important and dynamic economic force that causes the urbanization of the population and the shift of farm workers to nonfarm activities. If labor were completely mobile, the income gaps would tend to be small. But the mobility of labor is often impeded by such factors as traditional ideologies and social systems, particularly during the early stages of economic development. Consequently it

1. Simon Kuznets, "Economic Growth and Income Inequality," American Economic Review, vol. 45, no. 1 (March 1955), pp. 1-28.

224 INCOME DISTRIBUTION AND ECONOMIC STRUCTURE 225 never is perfect. Because it is imperfect, part of the labor force remains in the lower productivity sectors and causes the gaps in income to widen between sectors. In Taiwan the income gap between farm and nonfarm families widened during 1964-72 because farm income was growing at a slower rate than nonfarm income. The income gap between rural and urban sectors also widened. But despite these widening gaps between sectors, the inequality of income significantly declined at the national level. How could this have happened? How could the inequality of income decline for the entire country as the inequality of incomeincreased between farm and nonfarm families? This chapter probes the reasons for that reduction in the inequality of family income by using a sectoral decomposition formula that measures two main effects: the inequality within sectors, and that among sectors. The root causes of the inequality of family income will thus be explained by analyzing an intersectoral effect and an intrasectoral effect. The intersectoral effect, constituted by a family-weight effect and an income-disparity effect, is caused by changes in the shares of different sectors in the total number of families and in total family income. The family-weight effect is caused by changes in the weights of sectors as measured by the percentages of families in each sector. When an economy develops and labor is reallocated, the modern sectors expand while the more traditional sectors shrink. This shift of family weights among sectors has an effect on the distribution of income. In contrast, the income-disparity effect is caused by changes in the income parities among sectors. The gap of average family income between two sectors principally arises from productivity differences. Because of the differences in the technology used in agricultural and nonagricultural production, labor productivity usually is higher and growing more rapidly in the modern sector than in the traditional sector. That, too, has an effect on the distribution of income. The intrasectoral effect is caused by changes in the inequality of income within each sector and is explained by numerous causative elements. Its principal cause, however, is the heterogeneity of families arising from differences in the ownership of assets and differences in the ownership of labor embodying particular characteristics. Thus, within each sector, it is possible to identify a number of social groups or classes of families based on the various types and quantities of physical and human assets owned by families. A group will 226 INCOME DISTRIBUTION AND ECONOMIC STRUCTURE be referred to as a homogeneousgroup. The heterogeneity of families in a sector can then be described by the coexistenceof homogeneous groups. This chapter is principally devoted to a study of the proximate causes of the reduction in the inequality of income in Taiwan. First, an equation for decomposition will be presented. Second, an attempt will be made to decompose national income according to classifications of income recipients by sector and homogeneous group. The sectoral classificationsare based on farm and nonfarm activity and on the degree of urbanization, proxied by rural, semiurban, and urban residence. The group classifications are based on the number of persons employed per family and on the age, sex, and educational background of the head of family. Third, changes in the inequality of income over time will be analyzed in relation to industrialization and urbanization through the divergence in the income-relative, which is the ratio of the sectoral share in total income to the sectoral share in total households, and through the decomposition of income recipients into homogeneousgroups. Fourth, demographic factors will be examined, and the causes of inequality identified in relation to the size and composition of families. The reduction in the inequality of income over time will be linked to changes in the size of families, the number of employed members per family, and the age, sex, and educational background of the head of family. Here, again, changes will be analyzed through the divergence in the income-relative for various sectors and the decomposition of income recipients into homogeneous groups. The analysis of the intrasectoral and intersectoral effects will show that the reduction in the inequality of income within the nonfarm sector was the essential cause of the nationwide reduction in the inequality of income. That is, the favorable intrasectoral effect for the nonfarm sector more than compensated for the adverse intersectoral effect and made it possible for the inequality of income to be reduced across the entire country. The findings, based on the analysis of intragroup and intergroup effects, indicate the importance of demographic and economic forces in reducing the inequality of income among families in Taiwan.

The Decomposition Equation

Kuznets used agricultural and nonagricultural family weights, as well as intersectoral and intrasectoral inequalities, to analyze the in- THE DECOMPOSITION EQUATION 227 terrelations between changes in the economic structure and the distribution of income.2 Swamy decomposed the coefficient of variation in the two-sector model.' The decomposition in this chapter follows this general line of reasoning, but is generalized to n sectors. The decomposition formula should separately identify the intrasectoral and intersectoral effects that contribute to overall income inequality. For this purpose, it helps if the inequality indicator of the whole economy can be explained in relation to such measures as the proportions of farm and nonfarm families, the mean incomes of the two sectors, and the indicators of income inequality of the two sectors. As an inequality indicator, the coefficient of variation is convenient for this purpose.' Now consider the whole economy [w] to comprise a farm sector [a] and a nonfarm sector [n]. In the example of figure 5.1, the three sectors [w, a, and n] are represented by the three frequency distributions corresponding to the data in table 5.1. This example illus- trates the type of data needed in this chapter. When there are two groups of income recipients (agriculture and nonagriculture) and k income classes, the variances for agriculture [Va], nonagriculture [Vs], and the whole economy [EV,] are defined as follows: b, k (5.1a) Va = L Pa(Yi - Ya),, Vn E Pi(Yi -

V.c =E Pj(Y -j )2, where: i=l (5.1b) f = i + fn; (i =1, 2, . ,k) Eclass frequency for whole economy 1 as sum of group frequencies ] k ~~~~~k (5.1c) fa fai f f f =fa +fn; i=l i=l

2. Kuznets, "Economic Growth and Income Inequality." 3. Subramanian Swamy, "Structural Changes and the Distribution of Income by Size: The Case of India," Review of Income and Wealth, vol. 12, no. 2 (June 1967), pp. 155-74. 4. It will be shown in chapter twelve that if the Gini coefficient were used for homogeneous group decomposition, a third term-for a crossover effect- would appear in addition to the intersectoral and intrasectoral effects. Conse- quently the coefficient of variation is used in this chapter to simplify the analysis. 228 INCOME DISTRIBUTION AND ECONOMIC STRUCTURE

Figure 5.1. Income Distribution for Agricultural, Nonagricultural, and All Sectors

6( _ 60- f a = agricultural sector n = nonagriculturalsector 50

0 40

D 30 L --- I

1 2 3 4 5 6 7 8 Income EY] Source: Table 5.1.

(5.1d) h,, = ff, h. = fn/f; (h. + h. 1 Egroup family shares] (5.1e) pai =1 faj/jf2- 3i_16pn =fi'lfn, Pi = haP'j+ h.P,.; (i 1,02, )

k k A; pai = ) EPi = 1) (EPi 1)

rrelative class frequencies]

k k ~~~~~~~~~~~k (5-1f) Ya.= iy,i Y. pyni, Yi,.= piyi

[incom means] = hy + h[yY by equation (5.1e). THE DECOMPOSITION EQUATION 22.9

Table 5.1. Numerical Example of Income Distribution for Agricultural, Nonagricultural, and All Sectors

Number of Number of households households Number of in agri- in nonagri- households Income Income Midpoint cultural cultural in all group range income sector sector sectors [i] [Y.] [fa] [fnd Ef = faS±fn

1 0.5-1.5 1 6 2 8 2 1.5-2.5 2 30 25 55 3 2.5-3.5 3 17 31 48 4 3.5-4.5 4 10 26 36 5 4.5-5.5 5 6 24 30 6 5.5-6.5 6 4 13 17 7 6.5-7.5 7 2 4 6

All groups - - 75 125 200

- Not applicable. Source:Constructed by the authors.

Itcan be readily shown that: (5.2a) Vt = A + B, where (5.2b) A = haVa + hnVn and 2 2 (5.2c) B = ha(yw - ya) + hn(Y. - y.) . In equation (5.2b) A is the weighted average of the group variances [V0 and Vn]; the group family shares [ha and h.] are the weights. In equation (5.2c) B is the variance of all households when, for each group, total income is redistributed such that every household receives the mean income of the group [Ya and y.]. The coefficients of variation for the two groups [Ia and I,,] and for the whole economy [Il] are defined as follows: (5.3) I. = V .Iw/yw, Ia = V-V/Ya, and I. = /y. Substituting these definitions in equation (5.2) gives: 2 (5.4a) I', = h.U2I2 + h0 U'In + ha(l - Ua)2 + hn(l - U0) , where: (5.4b) Ua = ya/yut and U, = y./yu. 230 INCOME DISTRIBUTION AND ECONOMIC STRUCTURE

In equation (5.4b) U0 and Up express the mean income of each group as a fraction of the mean income of the whole economy. Be- cause the object of this analysis is to assess the separate effects on I,Lof the variation of the group family shares [h.and h.], the group coefficients of variation [Ia and I.],and the group income parities [U, and U.], it is not convenient to use Ua and U.. The reason is that the family shares [ha and h.] enter into the definition of Yw in equations (5.1e) and (5.1f). The group income parities are defined as follows: (5.5a) Za = Ya/Y and Z. = ya/y, where (5.5b) y = (ya + Y.)/ 2 . These equations express the individual group means as a parity of the simple arithmetic average of the group means. Then:

(5.6a) U = Fa(Za, Z., h., ha) = Za(Z.+ Z.)/2(h.Z0 + hnZn) and (5.6b) Un = F (Z, Z.,ha, ha) = Zn(Za+ Z.)/2(haZa+ hnZn) by equations (5.4b), (5.5a), and (5.1f).

These equations show that U. and U. are functions of Z,, Z0, h., and hn.When Ua and U. in equation (5.5) are substituted in equation (5.4a): (5.7) IW = f(Ia, In,ha, h., Z.,Za). That is, I. is a function of I,, I,, h,, ha, Z., and Z.. If there are m groups of income recipients, equation (5.7) can be readily generalized as:

(5.8) IW= f(I,, I 2, ... ,Ij,..Im; h,h2,..., hj, hm; ZI) Z27... p Zip... J Zm). 1i is the coefficient of variation; h, is the family share; Z, is the income parity of the jth group. Treating these variables as functions of time, I. can be differentiated with respect to time to give:

(5.9a) dt = R + D, where (5.9b) >l jdt

(5.9b) R asectnald= d al181dt rintrasectoral effectj EMPIRICAL DECOMPOSITION BY SECTORS AND HOMOGENEOUS GROUPS 231

(5.9c) D = W + P, where [intersectoral effect]

(5.9d) W = (t-' =O) and j_,_ ah3 dt j- dt/ [family-weight effect]

(5.9e) p = Z dZ aZi dt [income-di8parity effect]

Empirical Decomposition by Sectors and Homogeneous Groups

The decomposition equation (5.4a) can be applied to decompose the nationwide coefficient I, for various kinds of sectoral classification. This application is part of the strategy in this chapter of seeking additional causal relations by way of an essentially inductive methodology. Because the Taiwanese economy is dualistic, the nationwide coefficient of variation will first be decomposed into coefficients for the farm and nonfarm sectors. This nationwide coefficient will also be decomposed into sectors classified by varying degrees of urbanization. Because the age, sex, and educational level of the family head are attributes that affect family income, the same decomposition equation will then be applied to the classification of these families according to each of these factors. It will also be applied to groups based on the number of persons employed per family. In summary, the decomposition equation will be applied to the following sectoral and group classifications: * Farm and nonfarm economic activity (two sectors) * Degree of urbanization (six sectors and three sectors) * Age of family head (six groups) . Sex of family head (two groups) * Educational level of family head (six groups) * Persons employed per family (seven groups)

For each decomposition the information needed is the coefficient of variation for the jth sector or group [I;], the proportion of families in the jth sector or group [hj], and the ratio of the income per family 232 INCOME DISTRIBUTION AND ECONOMIC STRUCTURE

Table 5.2. Decomposition Analysis, by Farm and Nonfarm Sectors, 1964-72

Variable and sector Notation 1964 1966 1968

Total Gini G 0.3282 0.3301 0.3348

Sectoral Gini Farm sector G, 0.3153 0.3264 0.2916 Nonfarm sector G2 0.3363 0.3315 0.3383

Total coefficient I 0.7493 0.7073 0.7939

Sectoral coefficient Farm sector 11 0.6524 0.6658 0.5952 Nonfarm sector 12 0.8035 0.7244 0.8109

Sectoral family fraction Farm sector hi 0.3959 0.3093 0.3154 Nonfarm sector h2 0.6041 0.6907 0.6846

Sectoral family income parity Farm sector ZA = yi/y 0.9888 0.9735 0.8350 Nonfarm sector Z2 = y2/y 1.0112 1.0265 1.1650

Estimated coefficient 7 0.7490 0.7087 0.7956

Error e = I-I -0.0003 0.0014 0.0017

Percentage error (percent) D e/I X 100 -0.04 0.20 0.21

Sources:Calculated from DGBAS data (Taiwan Province and Taipei City combined) for various years. of sector or group j to the average income per family of all sectors or groups EZ, = (y1/y)]. The results of each decomposition are shown in tables 5.2 through 5.8. The maximum error of estimation of equation (5.4a), expressed as a percentage of the original coefficient, is 1.69 percent among the seventeen estimates; the average error of estimation is 0.24 percent. EMPIRICAL DECOMPOSITION BY SECTORS AND HOMOGENEOUS GROUPS 233

1970 1971 1972 Notation Variable and sector

0.2991 0.3006 0.2953 G Total Gini

Sectoral Gini 0.2828 0.2974 0.2907 GI Farm sector 0.2852 0.2916 0.2876 02 Nonfarm sector

0.6120 0.6194 0.6021 I Total coefficient

Sectoral coefficient 0.5734 0.6218 0.6061 I, Farm sector 0.5822 0.6007 0.5857 I2 Nonfarm sector

Sectoral family fraction 0.3091 0.2363 0.2588 hi Farm sector 0.6909 0.7637 0.7412 h2 Nonfarm sector

Sectoral family income parity 0.8075 0.8464 0.8644 Z, = yi/y Farm sector 1.1925 1.1536 1.1356 Z2 = Y2/Y Nonfarm sector

0.6115 0.6199 0.6032 I Estimated coefficient

-0.0005 0.0005 0.0011 e = I-I Error

Percentage error -0.08 0.08 0.18 D = E/I X 100 (percent)

In all these tables the values of the sectoral and group Gini coefficients [Gi] and the Gini coefficient for all families [G] are shown for purposes of comparison.

Farm and nonfarm sectors It is interesting to compare the results shown in table 5.2 with the income inequalities, family fractions, and family income parities of 234 INCOME DISTRIBUTION AND ECONOMIC STRUCTURE

the DGBAS farm and nonfarm sectors used in chapter three. According to table 5.2 the situation in Taiwan over the 1964-72 period shows the following: * The inequality of the distribution of income was less within the farm sector than within the nonfarm sector before 1971 and slightly greater in 1971 and 1972. . The weight of the farm sector in the total declined. * The per family income of the nonfarm sector was higher than that of the farm sector. . The income distribution of the farm and nonfarm sectors improved, but the speed of improvement was less for the farm sector than for the nonfarm sector. The farm sector, which earlier showed less inequality than the nonfarm sector, showed more in 1972. These results, using segmentation rather than additive-components decomposition, are comparable to those obtained in chapter three.

Degree of urbanization Because of the importance of industrialization and urbanization in economic growth, the effect of urbanization on the distribution of income should be explored. This effect can be brought out more clearly with the help of the sectoral decomposition equation. The necessary data were compiled from the original questionnaires of the DGBAS surveys for 1966 and 1972. This compilation is divided into two parts. One model of six sectors is based on a county classification; another model of three sectors is based on a city-town-village classification. The six-sector classification is based on the degree of urbanization defined by a cluster of ratios: population to area, nonagricultural employment to area, nonagricultural wage to area, nonagricultural value added to area, government expenditure to area, nonagricultural capital to labor, nonagricultural wage to labor, nonagricultural value added to labor, nonagricultural employment to population, and agricultural products to total products. The three- sector classification is based on the definitions for urban, semiurban, and rural areas given by the DGBAS and used in chapter four. The two classifications have their respective merits and demerits. The six-sector classification has the merit that many economic indicators are available at this level, so that the characteristics of urbanization can be identified and analyzed in relation to these EMPIRICAL DECOMPOSITION BY SECTORS AND HOMOGENEOUS GROUPS 235 indicators. That six-sector classification nevertheless deemphasizes the geographic or locational dimension; for this reason a town may well be included in a rural area. The three-sector classification is separated by smaller units and brings out more clearly the underlying characteristics of urbanization. But its usefulness for economic analysis is limited because not even the information on value added is available by this classification. To identify the relations between urbanization and income distribution, the income data based on the city-town-village classification were compiled from the original questionnaires for 1966 and 1972. Tables 5.3 and 5.4 give the results of the six-sector and three-sector classifications and show the following for those two years:

. The inequality of the distribution of income within the more urban sectors was not necessarily worse than that within the less urban sectors. * The proportion of families in the most urban sector in the total increased, while that of the least urban sector declined over time. * The per family incomes of the more urban sectors generally were higher than those of the less urban sectors. * Income inequality within a sector improved for every sector over time.

Age of family head Table 5.5 indicates that the inequality of income distribution for each age category declined between 1964 and 1972. Moreover there seems to have been a tendency toward somewhat greater inequality for the higher age groups. As would be expected, earning power increased with age until age 60 and then declined.

Sex of family head The percentage distribution of female and male family heads in each income bracket shows that females make up a majority of family heads in the two lowest income groups; there are none in the highest income group. Thus the presence of female heads of households is associated with poverty. In Taiwan, as elsewhere, job opportunities for females have generally been far from equal to those for males. The jobs offered to women are also relatively less important, and thus provide lower incomes. Although a female's earning power 236 INCOME DISTRIBUTION AND ECONOMIC STRUCTURE

Table 5.3. Decomposition Analysis, by Degree of Urbanization in the Six-sector Classification, 1966 and 1972

Variableand sector Notation 1966 1972

Total Gini G 0.3237 0.3018 Sectoral Gini Most urban sector G1 0.3146 0.3052 Second urban sector G2 0.3066 0.2776 Third urban sector G1 0.2928 0.2566 Fourth urban sector G4 0.3325 0.2730 Fifth urban sector Gs 0.3183 0.2876 Most rural sector G6 0.3321 0.2924 Total coefficient I 0.6610 0.6290 Sectoral coefficient Most urban sector h1 0.6405 0.6406 Second urban sector 12 0.6380 0.5499 Third urban sector 1, 0.5745 0.5016 Fourth urban sector 14 0.6869 0.5455 Fifth urban sector I5 0.6665 0.5848 Sixth urban sector 1 0.6593 0.6202 Sectoral family fraction Most urban sector h, 0.2122 0.2195 Second urban sector h2 0.0952 0.1431 Third urban sector h3 0.1469 0.1917 Fourth urban sector h4 0.3111 0.2259 Fifth urban sector h5 0.1150 0.1496 Sixth urban sector h6 0. 1196 0.0702 Sectoral family income parity Most urban sector Z = yYi/y 1.1481 1.3740 Second urban sector ZI = Y2 /y 1.1073 1.1374 Third urban sector Z3 = yl/y 0.9095 0.9893 Fourth urban sector ZI = y4 /y 0.8993 0.8424 Fifth urban sector Z5 = Y6/y 1.0219 0.8677 Sixth urban sector Z6 = /Y 0.9138 0.7890 Estimated coefficient I 0.6620 0.6297 Error = I-1 0.0010 0.0007 Percentage error (percent) D e/I X 100 0.15 0.11 Note: The total Gini coefficientand the coefficientof variation differ from those in tables 5.2 and 5.5-5.8 becausethe onesused here are directly calculated from the originalquestionnaires. Sources: Calculated from the original questionnairesof the DGBAS surveys. EMPIRICAL DECOMPOSITION BY SECTORS AND HOMOGENEOUS GROUPS 237

Table 5.4. Decomposition Analysis, by Degree of Urbanization in the Three-sector Classification, 1966 and 1972

Variable and sector Notation 1966 1972

Total Gini G 0.3237 0.3018

Sectoral Gini Urban sector G, 0.3134 0.2974 Semiurban sector G2 0.3182 0.2719 Rural sector G3 0.3316 0.2800 Total coefficient I 0.6610 0.6290

Sectoral coefficient Urban sector I1 0.6505 0.6182 Semiurban sector I2 0.6432 0.5433 Rural sector 13 0.6684 0.5628 Sectoral family fraction Urban sector hi 0.2826 0.3798 Semiurban sector h2 0.4137 0.3434 Rural sector h3 0.3037 0.2768 Sectoral family income parity Urban sector Zi = yi/y 1.1278 1.2632 Semiurban sector Z2 = Y2/Y 0.9245 0.9223 Rural sector Z3 = YJ/y 0.9477 0.8145

Estimated coefficient I 0.6615 0.6291

Error = I-I 0.0005 0.0001

Percentage error (percent) D e/I X 100 0.08 0.02

Note: Same as to table 5.3. Sources: Same as for table 5.3.

on average is less than that of a male, the data compiled by sex of head of household distort the real earning power of a female (table 5.6). In the ordinary family, the husband's name is registered as the head of his family, which results in the large proportion of male heads in the total. For the distribution of income, a family headed by a female has broader implications than its literal meaning. Such a family is most likely to be headed by a single woman or a widow; 238 INCOME DISTRIBUTION AND ECONOMIC STRUCTURE

Table 5.5. DecompositionAnalysis, by Age of Head of Family, 1964 and 1972

Variable and age Notation 1964 1972

Total Gini G 0.3282 0.2953 Sectoral Gini Under 20 years GI 0.3289 0.2645 20-30 years G2 0.3131 0.2875 30-40 years 03 0.2995 0.2672 40-50 years G4 0.3227 0.2817 50-60 years G5 0.3401 0.3150 Over 60 years G6 0.4107 0.4038 Total coefficient 1 0.7493 0.6021 Sectoralcoefficient Under 20 years I, 0.6280 0.5122 20-30 years I2 0.7867 0.5840 30-40 years 13 0.6364 0.5434 40-50 years I4 0.8244 0.5798 50-60 years I, 0.6933 0.6287 Over 60 years I6 0.8407 0.7971 Sectoralfamily fraction Under 20 years hi 0.0083 0.0090 20-30 years h2 0.1136 0.0956 30-40 years h3 0.3274 0.2916 40-50 years h4 0.3181 0.3582 50-60 years h, 0.1721 0.1839 Over 60 years h6 0.0605 0.0617 Sectoralfamily income parity Under 20 years Z, y,/y 0.6388 0.7758 20-30 years Z2 Y2 /Y 0.9437 0.9577 30-40 years Z3 y3/y 0.9893 0.9862 40-50 years Z4 - y4 /y 1.0833 1.0876 50-60 years Z= y6 /y 1.2130 1.1681 Over 60 years Z= Y6 /Y 1.1318 1.0245 Estimated coefficient I 0.7519 0.6029

Error e = I - I 0.0026 0.0008 Percentage error (percent) D = elI X 100 0.35 0.13

Sources: Same as for table 5.2. EMPIRICAL DECOMPOSITION BY SECTORS AND HOMOGENEOUS GROUPS 239

Table 5.6. Decomposition Analysis, by Sex of Head of Family, 1964 and 1972

Variable and sex Notation 1964 1972

Total Gini G 0.3282 0.2953

Sectoral Gini Male G, 0.3245 0.2899 Female G2 0.3575 0.3617

Total coefficient I 0.7493 0.6021

Sectoral Coefficient Male 1, 0.7591 0.5953 Female I, 0.7511 0.7239

Sectoral family fraction Male h, 0.9235 0.9327 Female h2 0.0765 0.0673

Sectoral family income parity Male ZA = yi/y 1.1173 1.0722 Female Z2= =Y/Y 0.8827 0.9278

Estimated coefficient I 0.7620 0.6039

Error e= I-I 0.0127 0.0018

Percentage error (percent) D E/I X 100 1.69 0.30

Sources: Same as for table 5.2. in the absence of a male spouse, the number of working persons in the family may be less than that in a family with a male head. These factors, when added to the lower earning power of the female, make the income parity of female-headed households lower than that of male-headed households.

Number of persons employed per family The number of persons employed per family is considered to be an important factor affecting family income and its distribution. The 240 INCOME DISTRIBUTION AND ECONOMIC STRUCTURE

Table 5.7. Decomposition Analysis, by Number of Persons Employed in Family, 1964 and 1972

Variableand number employed Notation 1964 1972

Total Gini G 0.3282 0.2953

Sectoral Gini None GI 0.4889 0.4297 1 G2 0.3213 0.2877 2 G3 0.3232 0.2805 3 G4 0.2968 0.2949 4 Gs 0.3158 0.2740 5 G6 0.2655 0.2415 6 or more G7 0.2785 0.2682

Total coefficient I 0.7493 0.6021

Sectoral coefficient None I, 1.0472 0.8999 1 I2 0.7316 0.6102 2 I3 0.7018 0.5645 3 14 0.5962 0.5892 4 is 1.0119 0.5719 5 I, 0.5497 0.4777 6 or more I7 0.5348 0.4942

conclusions from the decomposition effort are summarized in table 5.7.

. Income generally increased as the number of persons employed increased, which can be observed by comparing the income parity of each category. * Income inequality seems to have had a slight tendency to decline as the number of employed rose; the category, zero persons employed, had the widest income inequality.

Educational level of family head As already seen with respect to the explanation of the distribution of the wage share in chapter four, the effect of education on the level and distribution of income is crucial. The data reveal that illiterates EMPIRICAL DECOMPOSITION BY SECTORS AND HOMOGENEOUS GROUPS 241

Table 5.7 (Continued)

Variable and number employed Notation 1964 1972

Sectoral family fraction None h, 0.0140 0.0185 1 h2 0.3929 0.4218 2 h3 0.2760 0.3220 3 h4 0.1464 0.1206 4 h6 0.0895 0.0686 5 h6 0.0434 0.0295 6 or more h7 0.0378 0.0190

Sectoral family income parity None Z = yi/y 0.5818 0.6121 1 Z2= Y21Y 0.8129 0.8228 2 Z3 = y3/y 0.8816 0.9104 3 Z4= Y4/Y 0.9167 1.0947 4 Zs = Y /y 1.0964 1.0606 5 Z6= Y6/y 1.1460 1.1121 6 or more Z7= y7/y 1.5646 1.3873

Estimated coefficient 1 0.7552 0.6037

Error e = I - I 0.0059 0.0016 Percentage error (percent) D = e/I X 100 0.79 0.27

Source: Same as for table 5.2. had the least earning power (table 5.8). They were followed in ascending order by graduates of primary school, junior high school, and senior high and vocational school. The highest income could generally be earned by college graduates, not by graduate school graduates. The relation between wealth and higher levels of education is known not to be close.5 Although educational attainments up to a point are required for obtaining higher incomes, a person's income-earningability does not seem to be monotonically related to

5. Shirley W. Y. Kuo, "Income Distribution by Size in Taiwan Area-Changes and Causes," in Income Distribution, Employment and Economic Developmentin Southeast and East Asia, 2 vols. (Tokyo: Japan Economic Research Center, 1975), vol. 1, pp. 80-146. 242 INCOME DISTRIBUTION AND ECONOMIC STRUCTURE

Table 5.8. DecompositionAnalysis, by Educational Level of Head of Family, 1972

Variable and educationallevel Notation 1972

Total Gini G 0.2820 Sectoral Gini Graduate school graduate GI 0.1852 College graduate G2 0.2438 Senior high school graduate GS 0.2547 Junior high school graduate G4 0.2521 Primary school graduate G, 0.2769 Illiterate G6 0.3059 Total coefficient I 0.5651 Sectoralcoefficient Graduate school graduate II 0.3450 College graduate 12 0.4725 Senior high school graduate Ih 0.5132 Junior high school graduate 14 0.5062 Primary school graduate I, 0.5627 Illiterate 16 0.5895 Sectoralfamily fraction Graduate school graduate h, 0.0011 Collegegraduate h2 0.0706 Senior high school graduate h3 0.1607 Junior high school graduate h4 0.1301 Primary school graduate h5 0.5141 Illiterate h6 0.1234 Sectoralfamily income parity Graduate school graduate Z= yi/y 1.1247 College graduate Z2 Y2/Y 1.1840 Senior high school graduate Z3= yS/y 1.1458 Junior high school graduate Z4 = y4/y 0.9626 Primary school graduate ZA = y/y 0.8505 Illiterate Z = Y6/Y 0.7324 Estimated coefficient I 0.5635 Error e=I-I -0.0016 Percentage error (percent) D = c/I X 100 -0.28

Source: Calculated from DGBAS data. Only 1972 data for Taiwan Province is available. CHANGES IN INCOME INEQUALITY 243 education beyond a certain income level. What is more interesting, the equity of income distribution tends to be higher for the more educated groups.

Changes in Income Inequality Associated with Industrialization and Urbanization

During the 1964-72 period, as already seen, overall income inequality significantly declined. But with farm-family income growing less rapidly than nonfarm-family income, the income gap between the two kinds of family widened. In addition, the income gaps among family groups in different locations, classifiedby the degree of urbanization, widened during the same period. The widening gap caused by industrialization and urbanization can be observed through changes in income disparities, an indicator suggested by Kuznets, in sectors classified by farm and nonfarm families and by different degrees of urbanization.6 Disparities in the shares of farm and nonfarm families increased from 1964 to 1972, indicating increasing inequality between the two sectors (table 5.9). The respective divergence of the income-relative from unity in each sector also shows increasing inequality. Income disparities by degree of urbanization show that the widening was mainly caused by the most urban and rural sectors (tables 5.10 and 5.11). Levels and trends in income differences among the sectors reveal that per family income was rising at a higher-than-average rate in the nonfarm sector and the most urban sector. In contrast, per family income was rising at a lower-than-average rate in the farm sector and the most rural sector. How, then, was more equity generated for the whole economy? In an attempt to answer this question, equation (5.9) was used to determine intrasectoral and intersectoral effects for the 1964-72 period.7 The intersectoral effect will be further divided into a family-

6. Simon Kuznets, "Demographic Components in Size Distribution of Income," in Income Distribution, Employment and Economic Developmentin Southeast and East Asia, vol. 2, pp. 389-472. 7. In earlier chapters 1968 was identified as the turning point for growth and distribution. In this regard separate causal analyses should be made for the 1964-68 and 1968-72 subperiods. We nevertheless restrict ourselves to the entire 1964-72 period because the data required for the separate analysis of causal subperiods are lacking. For example, data on urbanization can be used only for 1966 and 1972. 244 INCOME DISTRIBUTION AND ECONOMIC STRUCTURE

Table 5.9. Income Disparities, by Farm and Nonfarm Families, 1964 and 1972

Share of Share of Disparity income families in shares Income (percent) (percent) (percentagepoints) relativea Type of family 1964 1972 1964 1972 1964 1972 1964 1972

Farm families 39.1 21.0 39.6 25.9 -0.5 -4.9 0.99 0.81 Nonfarm families 60.9 79.0 60.4 74.1 0.5 4.9 1.01 1.07

All families 100.0 100.0 100.0 100.0 1 . 0b 9.8b 1.00 1.00

Sources: Same as for table 5.2. a. The ratio of the share of income to the share of families. b. The sum of the absolute values.

Table 5.10. Income Disparities, by Degree of Urbanization in the Six-sector Classifcation, 1966 and 1972

Share of Share of Disparity income families in shares Income (percent) (percent) (percentagepoints) relative, Degree of urbanization 1966 1972 1966 1972 1966 1972 1966 1972

Most urban 24.6 29.3 21.2 21.9 3.4 7.4 1.16 1.34 Second urban 10.7 15.8 9.5 14.3 1.2 1.5 1.13 1.10 Third urban 13.5 18.4 14.7 19.2 -1.2 -0.8 0.92 0.96 Fourth urban 28.3 18.5 31.1 22.6 -2.8 -4.1 0.91 0.82 Fifth urban 11.9 12.6 11.5 15.0 0.4 -2.4 1.03 0.84 Most rural 11.0 5.4 12.0 7.0 -1.0 -1.6 0.92 0.77

All sectors 100.0 100.0 100.0 100.0 1 0 . 0 b 1 7.Sb 1.00 1.00

Sources: Same as for table 5.3. a. The ratio of the share of income to the share of families. b. The sum of the absolute values. CHANGES IN INCOME INEQUALITY 245

Table 5.11. Income Disparities, by Degree of Urbanization in the Three-sector Classification, 1966 and 1972

Share of Share of Disparity income families in shares Inconw (percent) (percent) (percentagepoints) relative Degreeof urbanization 1966 1972 1966 1972 1966 1972 1966 1972

Urban 32.2 46.9 28.2 38.0 4.0 8.9 1.14 1.23 Semiurban 38.7 31.0 41.4 34.3 -2.7 -3.3 0.93 0.90 Rural 29.1 22.1 30.4 27.7 -1.3 -5.6 0.96 0.80

All sectors 100.0 100.0 100.0 100.0 8.0b 17.8b 1.00 1.00

Sources: Same as for table 5.3. a. The ratio of the share of income to the share of families. b. The sum of the absolute values.

weight effect and an income-disparity effect. The change in the nationwide inequality depends on the sum of these effects and cannot be explained by any single one.

Causes traced to the farm-nonfarm decomposition The intrasectoral and intersectoral effects calculated for the farm and nonfarm sectors are shown in table 5.12. * Because of the reduction in internal inequality within both the farm and nonfarm sectors, the favorable intrasectoral effect contributed to the reduction in income inequality. The farm sector contributed 7 percent to the intrasectoral effect; the nonfarm sector 93 percent. * The intersectoral effect, constituted by the adverse family- weight effect and the adverse income-disparity effect, was adverse to the distribution of income. The family-weight effect contributed 26 percent to the intersectoral effect; the income disparity effect 74 percent. That is, the change in the weights of farm and nonfarm family numbers and the widening of the income gap between the two sectors adversely affected the distribution of income. The magnitude of adverse effects, expressed as a percentage of the absolute value of the total change, was 18.1 percent. 246 INCOME DISTRIBUTION AND ECONOMIC STRUCTURE

Table 5.12. Causes of the Reduction in Income Inequality, by Farm and Nonfarm Sectors,1964-72

Intra- Inter- Family Income Total sectoral sectoral = weight + disparity effect effect, effect effect effect [2aI-.dIl 1 aL. .dAlh F al. dZ Sector [i] IY ali dJ + Lj a dtj Both sectors -0.1457 -0.172 7 0.0270 0.0057 0.0213 Percentage of total effect -100.0 -118.5 18.5 3.9 14.6 Farm sector - -0.0117 (-6.8) - 0.0512 0.0115 Nonfarm sector - -0.1610 (-93.2) - -0.0455 0.0098

- Not applicable. Note:Positive coefficientsrepresent effectswhich act to increase income inequality; negative coefficients,those which act to reduceincome inequality. Source:Calculated from table 5.2. a. The figuresin parentheses indicate the percentage compositionof the intrasectoral effect.

The decomposition of the intrasectoral and intersectoral effects shows that the essential cause of the reduction in income inequality in Taiwan was the reduction in income inequality within the nonfarm sector. That is, the reduction in intrasectoral inequality within the nonfarm sector more than compensated for the adverse intersectoral effect and made possible the reduction in income inequality for the total economy.

Causes tracedto the urbanization decomposition The causes of the overall reduction in income inequality related to the degree of urbanization are examined next (table 5.13). The following intrasectoral and intersectoral effects were observed: - The reduction in internal inequality within each of the six sectors contributed most to the reduction in income inequality. The rate of contribution to the reduction in income inequality of the total economy was 183.7 percent. The reduction in intra- CHANGES IN INCOME INEQUALITY 247

Table 5.13. Causesof the Reduction in Income Inequality, by Degree of Urbanizationin the Six-sectorClassification, 1966-72

Intra- Inter- Family Income Total sectoral sectoral = weight + disparity effect effect' effect effect effect

r[tua1 sl r2]Praldh,k|d, + 2 aIwdZj]

Sector [ I] lhdt I l oh1 dt j L,aZidtJ

All sectors -0.0332 -0.0610 0.0278 -0.0066 0.0344 Percentage of total effect -100.0 -183.7 83.7 -19.9 103.6

Most urban - -0.00003 (0.0) - -0.0018 0.0259 Second urban - -0.0118 (-19.4) - -0.0175 0.0004 Third urban - -0.0091 (-14.9) - -0.0181 -0.0042 Fourth urban - -0.0282 (-46.2) - 0.0267 0.0047 Fifth urban - -0.0091 (-14.9) - -0.0110 0.0040 Most rural - -0.0028 (-4.6) - 0.0151 0.0036

- Not applicable. Note: Positive coefficients represent effects which act to increase income inequality; negative coefficients, those which act to reduce income inequality. Source: Calculated from table 5.3. a. The figures in parentheses indicate the percentage composition of the intrasectoral effect.

sectoral inequality compensated for the adverse intersectoral effect and thus significantly contributed to the reduction of income inequality for the whole economy. . The fourth urban sector made the highest contribution to the intrasectoral effect, recording 46.2 percent of the total. Other important contributions came from the second, third, and fifth urban sectors; their contribution rates ranged from 14.9 percent to 19.4 percent. The most rural sector contributed 4.6 percent; the most urban sector contributed nothing. This seems to indicate that the income inequality was reduced much more within a semiurban area than within either the most urban or the most rural area. * The intersectoral effect was unfavorable to the reduction of income inequality. Combining the family-weight effect and the income-disparity effect, the total adverse contribution was 83.7 percent. 248 INCOME DISTRIBUTION AND ECONOMIC STRUCTURE

Table 5.14. Causes of the Reduction in Income Inequality, by Degree of Urbanization in the Three-sector Classification, 1966-72

Intra- Inter- Family Income Total sectoral sectoral = weight + disparity effect effect' effect effect effect [ a .il 2d al-.dh,1 + [2 aI_ dZj] Sector Ii Lj al; dt I ahi dt LaZi dt

All sectors -0.0334 -0.0679 0.0345 0.0049 0.0296 Percentage of total effect -100.0 -203.3 103.3 14.7 88.6

Urban - -0.0151 (-22.2) - -0.0279 0.0179 Semiurban - -0.0296 (-43.6) - 0.0245 0.0002 Rural - -0.0232 (-34.2) - 0.0083 0.0115

- Not applicable. Note: Positive coefficients represent effects which act to increase income inequality; negative coefficients, those which act to reduce income inequality. Source: Calculated from table 5.4. a. The figures in parentheses indicate the percentage composition of the intrasectoral effect.

. The change in the weights of family numbers had a moderately favorable effect on the reduction of income inequality for the total economy. . The widening income gaps among the six sectors adversely affected the distribution of income. The magnitude of the adverse income-disparity effect, expressed as a percentage of the absolute value of the total change, was 103.6 percent.

Another observation for the effects of urbanization on the distribution of family income is based on the three-sector classification of cities, towns, and villages. Causes of reduction in income inequality observed by this three-sector classification are presented in table 5.14. Essentially the results are the same as those observed with the six-sector classification.

. The favorable intrasectoral effect more than compensated for the adverse intersectoral effect. * The contribution by the semiurban sector to the intrasectoral effect was largest; that by the urban sector, smallest. ADDITIONAL REFLECTIONS 249

The intersectoral effect was adverse to the reduction of income inequality. Based on this city-town-village classification, the change in the family weight had a slightly adverse effect on the change in income equality. In summary, the intersectoral income gap widened during the course of industrialization and urbanization in Taiwan, but intrasectoral inequality was reduced more than enough to compensate for the adverse intersectoral effect. This performance confirms that decentralization of economic development may contribute substantially to the reduction of income inequality.

Additional Reflections

Rapid economic growth in Taiwan during the 1964-72 period raised the average income of households in every bracket and led to absolute increases in the welfare of all income groups. What are the policies that seem to have contributed to TI'aiwan's success in reducing income inequality during a period of rapid growth? Many, to be sure. But some of the more important and obvious policies are the following: the pursuit of a labor-intensive and outward-looking growth path; early land reform; the reduction in the collection of a hidden tax on rice; and reductions in the relative tax burden of farmers and the poor. Moreover, the size and composition of families moved in a direction favorable to a reduction of income inequality. The causal interrelations among these and other factors still are far from clear and require further analysis.

The importance of rural by-employment As noted in chapter three, a distinguishing characteristic of Tai- wan's farm-family income is that it has a substantial component of nonagricultural income. The proportion of nonagricultural income in farm income was 34.1 percent in 1964 and 53.7 percent in 1975. How did the composition of nonagricultural income relate to different levels of farm income? The lower the income level, the bigger the proportion of nonagricultural income (table 5.15). In 1975 the lowest 80 percent of families received more than half their income from nonagricultural sources. About 98 percent of nonfarm income 260 INCOME DISTRIBUTION AND ECONOMICSTRUCTURE

Table 5.15. Sources of Income of Farm and Nonfarm Families, by Decile, 1966 and 1976 (percent)

Composition of total family income

1966 1975

Nonfarm Nonfarm Farm families families Farm families families

Non- Non- Non- Non- Agri- agri- Agri- agri- Agri- agri- Agri- agricultural cultural cultural cultural cultural cultural cultural cultural Decile, income income income income income income income income

1 54.7 45.3 2.9 97.1 33.9 66.1 2.1 97.9 2 55.3 44.7 2.8 97.2 37.3 62.7 2.0 98.0 3 57.3 42.7 3.0 97.0 39.0 61.0 2.1 97.9 4 61.0 39.0 2.4 97.6 40.6 59.4 1.9 98.1 5 64.3 35.7 1.8 98.2 43.1 56.9 1.6 98.4 6 65.5 34.5 2.4 97.6 44.4 55.6 1.9 98.1 7 68.5 31.5 1.7 98.3 46.0 54.0 1.8 98.2 8 70.1 29.9 2.2 97.8 48.4 51.6 2.7 97.3 9 70.2 29.8 2.3 97.7 50.8 49.2 1.9 98.1 10 67.6 32.4 1.8 98.2 52.4 47.6 2.4 97.6 All deciles 65.9 34.1 2.2 97.8 46.3 53.7 2.1 97.9

Sources: Calculated from DGBAS, Report on the Survey of Family Income and Expenditure,1966 and 1975. a. Arranged from lowest to highest income.

was from nonagricultural activities. Thus the role of agricultural income in nonfarm household income was negligible. During the 1964-75 period the real income of both farm and nonfarm families considerably increased in every income bracket. The increase was much higher in the lower income groups than in the higher income groups (table 5.16). For the nonfarm sector, the lowest decile had a 368 percent increase in income; the highest decile a 199 percent increase. For the farm sector, the lowest decile had a 235 percent increase in income; the highest decile had only a 17 percent increase. Furthermore, the increase of nonagricultural income brought about the increase in total farm-family income. The higher growth rates of income from nonagricultural activities ADDITIONAL REFLECTIONS 251

Table 5.16. Growth of Income of Farm and Nonfarm Families, by Decile, 1966-75 (percent) Farm families Total Agri- Nonagri- income of Total cultural cultural nonfarm Decilea income income income families

1 235 107 388 368 2 251 137 392 335 3 238 130 382 315 4 232 121 406 303 5 228 120 423 298 6 213 112 405 290 7 202 103 417 278 8 185 97 392 262 9 182 104 367 240 10 170 110 297 199 All deciles 199 110 372 261

Sources: Same as for table 5.15. a. Arranged from highest to lowest income.

among the lower-income family groups give additional support to the notion that two main factors were responsible for the good overall performance: the relatively rapid rate of employment generation for members of the lower income groups initially; the change in their wages subsequently. During the period under observation, rapid labor absorption finally eliminated rural unemployment or underemployment. Newcomers and unemployed individuals were mainly absorbed by the nonagricultural sector, particularly by light manufacturing industries. Thus unskilled labor was efficiently used. As the economy grew, such labor became relatively more scarce, until wage rates of unskilled labor finally were rising more rapidly than those of skilled labor. Undoubtedly the early and rapid absorption of unskilled labor substantially contributed to the rise in relative incomes of the lower income families, both urban and rural. Indus- trial decentralization clearly contributed to this labor absorption and was an essential factor contributing to the reduction of overall income inequality. 252 INCOME DISTRIBUTION AND ECONOMIC STRUCTURE

Table 5.17. Gini Index of Land Concentration in Selected Countries, Comparisons for Various Years

Decline in Gini Gini Gini index Country Year index Year index (percent)

Colombia 1960 0.864 1969 0.818 5.32 India 1953-54 0.628 1960-61 0.589 6.14 Mexico 1930 0.959 1960 0.694 27.64 Philippines 1948 0.576 1960 0.534 7.26 Taiwan 1952 0.618 1960 0.457 26.08 United Arab Republic 1952 0.810 1964 0.674 16.74

Source:Hung-Chao Tai, Land Reformand Politics (Berkeley: University of California Press, 1974), p. 310, reproduced in Yung Wei, "Modernization Process in Taiwan: An Allocative Analysis," Asian Survey, vol. 16, no. 3, (March 1976), pp. 249-69.

Effects of land reform Income inequality is naturally related to initial conditions. That is, it is related to the original distribution of such assets as land, capital, and educational training, which provide rents, dividends, interest, and salaries. The inequality usually is much more severe in asset holdings than in income. For these reasons, measures to dis- tribute assets more equally may be important for a more equal distribution of income. Table 5.17 shows the Gini index of land concentration in selected countries. The Gini index for Taiwan was 0.618 in 1952, before land reform had its full effect, and 0.457 by 1960.8 Taiwan's land reform, already discussed in chapter two, resulted in smaller scale farming. Landholdings of more than three hectares constituted 42 percent of the total cultivated area before land reform, but only 23 percent after its implementation. Landholdings of one hectare or less, which originally constituted 25 percent of the total area, increased to 35 percent. The smaller average size farms in turn brought about a more intensive use of labor and of multiple-cropping practices.

8. Yung Wei, "Modernization Process in Taiwan: An Allocative Analysis," Asian Survey, vol. 16, no. 3 (University of California Press, March 1976), pp. 249-69. ADDITIONAL REFLECTIONS 258

Table 5.18. Indexes of the Productivity of Land and Labor in Agriculture, Taiwan, 1950 and 1955

Land Land Labor Labor Year area productivity inputs productivity 1950 100.0 100.0 100.0 100.0 1955 100.7 121.5 107.6 113.2

Source: T. H. Lee, "Impact of Land Reform on the Farm Economy Structure," (n.p., n.d.).

After the land reform, farmers had a freer choice of crops. As owner-cultivators, they were under no obligation to produce rice for rental payments. Thus the land reform tended to reduce the share of rice and to increase the share of other such crops of higher value as livestock and poultry. Moreover labor productivity increased more slowly than land productivity during 1950-55, indicating the labor-using bias of technological change in agriculture (table 5.18).

Reduction in the collection of the hidden tax on rice For market control, all commercial activities of farmers' associations and private rice dealers in Taiwan were subject to government supervision. Control of rice not only stabilized the supply and price of rice, but also generated considerable revenue for government. A hidden tax on rice was imposed through land taxes, compulsory rice purchases, a rice-fertilizer barter system, and the payment for land in kind. All these taxes were levied by government purchases at lower-than-market prices. The revenue from these hidden taxes was important: it exceeded total income tax collections every year before 1963, but declined gradually after 1964 and rapidly after 1969, especially in comparison with the income tax. This rapid reduction in the collection of the hidden tax on rice undoubtedly contributed to the more even distribution of income over time.

Relative reduction in the tax burden of farm families The ratio of the tax burden of farm families to that of nonfarm families was 1.73 to 1 in 1966; it declined to 0.35 to 1 by 1975 (table 5.19). Even more noteworthy is that the reversal from farm families having a heavier to a lighter tax burden than nonfarm families was more pronounced for the lower income brackets. A cross-sectional 254 INCOME DISTRIBUTION AND ECONOMIC STRUCTURE

Table 5.19. Relative Tax Burden of Farm and Nonfarm Families, by Income Range, 1966 and 1975

Ratio of tax burdenof farm families to thatof nonfarm Incomerange families (thousandsof N.T. dollars) 1966 1975

Less than 10 3.92 10-20 3.60 0.85 20-30 3.22 1.16 30-40 2.59 1.39 40-50 1.67 1.34 50-60 2.07 1.12 60-70 2.02 0.95 70-80 1.42 0.83 80-90 1.31 0.82 90-100 0.68 0.60 100-150 0.68 0.49 150-200 1.17 0.56 More than 200 - 0.19 All income ranges 1.73 0.35

-Not applicable. Sources: Calculated from DGBAS, Report on the Survey of Family Income and Expenditure, 1966 and 1975. analysis of the relation of taxes to distribution is discussed in the next chapter.

Changingsize and compositionof families In chapter four on the inequality of family wage income, the causes of inequality were related to the size and composition of families. Some additional inductive evidence is cited here to support that analysis. These observations are based, however, on total family income, not on family wage income. How can the reduction in income inequality during the 1964-72 period be traced to changes in the size of families, the number of employed per family, the age of the family head, and the sex of the family head? Because the income gap widened between the farm and nonfarm sectors, it is desirable to keep the two sectors separate, lest the positive and negative demographic effects of each sector act ADDITIONAL REFLECTIONS 255 to compensate each other. But because of the lack of sectorally separated data for demographic effects on the distribution of income, these effects are observed in a combined framework that takes into account the whole economy. The income disparities by the number of employed, by age, and by sex are calculated. The causes of the reduction in the income inequality are also identified, based on the decomposition equation for each classification. All statistical results are shown in tables 5.20-5.29 appended to this chapter. During 1966-72 the average family sizes for the total economy, farm families, and nonfarm families all declined.9 The variance of family size also declined for each kind of family. The reduction of family size and its variance thus increased the homogeneity of family composition, a pattern that may have contributed to the reduction of income inequality. When the income disparity by size of family is calculated for the total economy, the results show that income disparities between various sizes of families considerably narrowed during the period. The disparities were mostly reduced by changes in the incomes of one-person families and of the family group of ten persons or more. The income disparities by number employed per family also declined. The greatest reduction of disparities occurred in family groups with the larger numbers of employed. Using the same decomposition formula to calculate the three effects, it is found that all of them contributed to the reduction of overall income inequality. The family-weight effect contributed 1.3 percent; the income-disparity effect 5.9 percent; the intrasectoral effect 92.8 percent. The income disparities by age of family head slightly declined. The reduction mainly resulted from the groups of under 20, 50-60, and over 60. The income disparities classified by sex of family head also declined. The per family income share of female-headed families rose during the period. The decomposition analysis shows that, whereas all effects contributed to the reduction in income inequality, the intrasectoral effect was dominant. In brief, when families are classified by size or composition, a reduction in income disparities is observed between groups in every case. The intrasectoral effect was dominant in each of the three cases. A favorable intersectoral effect is also observed in every case,

9. The year 1966 is observed because of the inadequacy of the relevant DGBAS data for 1964. We are grateful to Professor Kuznets for pointing this out. 256 INCOME DISTRIBUTION AND ECONOMIC STRUCTURE but its magnitude was not large. This suggests that changes in the size and composition of families must have contributed to the reduction of income inequality. The picture is not clear, however, because many of these changes were in turn the result of economic growth and by no means exogenous. Because interrelations between demographic change and economic growth are close, the intrasectoral reduction in income inequality observed in the demographic classification must have been caused by a large number of economic factors that are still too complicated to be unraveled here. More theoretical work, departing from the preliminary inductive evidence gathered in this chapter, is required.

Table 5.20. Average Size of Families, by Income Bracket, 1966 and 1972

1966a /972b

Average Average Income bracket number of Deviation number of Deviation (thousands of persons in from the persons in from the N. T. dollars) family mean family mean

Less than 10 2.0 -3.9 1.2 -4.5 10-20 4.4 -1.5 2.7 -3.0 20-30 5.5 -0.4 4.4 -1.3 30-40 6.5 0.6 5.2 -0.5 40-50 7.9 2.0 5.5 -0.2 50-60 8.4 2.5 5.9 0.2 60-70 7.2 1.3 6.1 0.4 70-80 8.8 2.9 6.4 0.7 80-90 8.2 2.3 6.9 1.2 90-100 8.2 2.3 6.5 0.8 100-200 9.3 3.4 7.5 1.8 More than 200 4.2 -1.7 7.0 1.3 All brackets 5.9 - 5.7

-Not applicable. Note: The average sizes of family in the same income brackets may not be directly comparable for the two years because of a possible escalation in the income level in each bracket during the period. Sources: Calculated from DGBAs, Report on the Survey of Family Income and Expenditure,1966 and 1972. a. For 1966 the variance divided by the square of the mean is 0.0747. b. For 1972 the variance divided by the square of the mean is 0.0330. ADDITIONAL REFLECTIONS 257

Table 5.21. Average Size of Farm Families, by Income Bracket, 1966 and 1972

1966& 1 9 7 2b Average Average Income bracket number of Deviation number of Deviation (thousandsof personsin from the personsin from the N.T. dollars) family mean family mean

Lessthan 10 3.2 -4.0 2.0 -4.5 10-20 5.5 -1.7 3.2 -3.3 20-30 6.7 -0.5 5.0 -1.5 30-40 7.8 0.6 6.1 -0.4 40-50 8.8 1.6 6.7 0.2 50-60 9.7 2.5 7.0 0.5 60-70 9.1 1.9 7.6 1.1 70-80 11.6 4.4 8.2 1.7 80-90 9.5 2.3 8.8 2.3 90-100 11.8 4.6 9.1 2.6 100-200 13.9 6.7 10.1 3.6 More than 200 - - 9.9 3.4

All brackets 7.2 - 6.5 -

Not applicable. Note: The average sizes of family in the same income brackets may not be directly comparable for the two years because of a possible escalation in the income level in each bracket during the period. Sources: Same as for table 5.20. a. For 1966 the variance divided by the square of the mean is 0.0709. b. For 1972 the variance divided by the square of the mean is 0.0583. 258 INCOME DISTRIBUTION AND ECONOMIC STRUCTURE

Table 5.22. Average Size of Nonfarm Families, by Income Bracket, 1966 and 1972

19668 19 7 2b

Average Average Income bracket number of Deviation number of Deviation (thousands of persons in from the persons in from the N. T. dollars) family mean family mean

Less than 10 1.6 -3.7 1.1 -4.2 10-20 3.8 -1.5 2.0 -3.3 20-30 5.0 -0.3 3.7 -1.6 30-40 6.0 0.7 4.7 -0.6 40-50 7.4 2.1 5.1 -0.2 50-60 7.8 2.5 5.5 0.2 60-70 6.5 1.2 5.7 0.4 70-80 7.5 2.2 5.8 0.5 80-90 7.4 2.1 6.5 1.2 90-100 7.3 2.0 6.1 0.8 100-200 7.1 1.8 6.9 1.6 More than 200 4.2 -1.1 6.1 0.8

All brackets 5.3 - 5.3 -

- Not applicable. Note: The average sizes of family in the same income brackets may not be directly compaxable for the two years because of a possible escalation in the income level in each bracket during the period. Sources: Same as for table 5.20. a. For 1966 the variance divided by the square of the mean is 0.0828. b. For 1972 the variance divided by the square of the mean is 0.0357. ADDITIONAL REFLECTIONS 259

Table 5.23. Income Disparities, by Size of Household, 1966 and 1972

Share of Share of Disparity income households in shares Income Number of (percent) (percent) (percentagepoints) relative, personsin household 1966 1972 1966 1972 1966 1972 1966 1972

1 2.6 1.4 6.6 3.3 -4.0 -1.9 0.39 0.42 2 4.3 2.8 5.4 4.2 -1.1 -1.4 0.80 0.67 3 5.8 7.8 7.7 9.3 -1.9 -1.5 0.75 0.84 4 9.7 12.5 11.5 13.7 -1.8 -1.2 0.84 0.91 5 14.0 20.9 15.3 21.2 -1.3 -0.3 0.92 0.99 6 14.5 19.5 14.8 19.3 -0.3 0.2 0.98 1.01 7 16.2 13.7 14.9 12.6 1.3 1.1 1.09 1.09 8 10.3 9.0 9.4 7.6 0.9 1.4 1.10 1.18 9 6.8 4.8 5.6 3.9 1.2 0.9 1.21 1.23 10 or more 15.8 7.6 8.8 4.9 7.0 2.7 1.80 1.55

All households 100.0 100.0 100.0 100.0 20.8b 12.6b 1.00 1.00

Sources: Same as for table 5.20. a. The ratio of the share of income to the share of households. b. The sum of tl - absolute values. 260 INCOME DISTRIBUTION AND ECONOMIC STRUCTURE

Table 5.24. Income Disparities, by Number of Persons Employed in Family, 1964 and 1972

Share of Share of Disparity Number of income families in shares Income persons (percent) (percent) (percentagepoints) relative, emrployedin family 1964 1972 1964 1972 1964 1972 1964 1972

None 1.2 1.2 1.8 1.8 -0.6 -0.6 0.67 0.67 1 37.3 37.9 42.2 42.2 -4.9 -4.3 0.88 0.90 2 27.9 32.0 29.1 32.2 -1.2 --0.2 0.96 0.99 3 11.8 14.4 11.1 12.1 0.7 2.3 1.06 1.19 4 11.5 8.0 S.9 6.9 2.6 1.1 1.29 1.16 5 5.2 3.6 4.0 2.9 1.2 0.7 1.30 1.24 6ormore 5.1 2.9 2.9 1.9 2.2 1.0 1.76 1.53

All families 100.0 100.0 100.0 100.0 13.4b 10.2b 1.00 1.00

Sources: Same as for table 5.2. a. The ratio of the share of income to the share of families. b. The sum of the absolute values. ADDITIONAL REFLECTIONS 261

Table 5.25. Causes of the Reduction in Income Inequality, by Number of Persons Employed in Family, 1964-72

Intra- Inter- Family Income Total sectoral sectoral = weight + disparity Number of effect effect, effect effect effect persons 2 aI,dI [ al. dhj] + r2dl,1dZ emfployeld [2] , tJ,d: 2 S ,ajd in family P3] Wi iT I L oh, dtJ L aZ-j -dl All categories -0.1532 -0.1422 -0.0110 -0.0020 -0.0090 Percentage of total effect -100.0 -92.8 -7.2 -1.3 -5.9

None - 0.0015(-1.0) - -0.0002 -0.0002 1 - -0.0395 (-27.8) - -0.0096 -0.0011 2 - -0.0371 (-26.1) - -0.0175 -0.0012 3 - -0.0010 (-0.7) - 0.0103 0.0008 4 - -0.0577 (-40.6) - 0.0022 -0.0024 5 - -0.0031 (-2.2) - 0.0070 -0.0002 6 or more - -0.0023 (-1.6) - 0.0058 -0.0047

- Not applicable. Note: Positive coefficients represent effects which act to increase income inequality; negative coefficients,those which act to reduce income inequality. Source: Calculated from table 5.7. a. The figures in parentheses indicate the percentage composition of the intrasectoral effect. 262 INCOME DISTRIBUTION AND ECONOMIC STRUCTURE

Table 5.26. Income Disparities, by Age of Head of Family, 1964 and 1972

Share of Share of Disparity income families in shares Income Age of (percent) (percent) (percentagepoints) relative, head of family 1964 1972 1964 1972 1964 1972 1964 1972

Under 20 0.5 0.7 0.8 0.9 -0.3 -0.2 -. 63 0.78 20-30 10.1 8.7 11.4 9.6 -1.3 -0.9 0.89 0.91 30-40 30.6 27.3 32.7 29.2 -1.1 -1.9 0.94 0.93 40-50 32.6 36.9 31.9 35.8 0.7 1.1 1.02 1.03 50-60 19.7 20.4 17.2 18.4 2.5 2.0 1.15 1.11 Over60 6.5 6.0 6.0 6.1 0.5 -0.1 1.08 0.98

All families 100.0 100.0 100.0 100.0 6 4 b 6.2b 1.00 1.00

Sources: Same as for table 5.2. a. The ratio of the share of income to the share of families. b. The sum of the absolute values.

Table 5.27. Causes of the Reduction in Income Inequality, by Age of Head of Family, 1964-72

Intra- Inter- Family Income Total sectoral sectoral = weight + disparity effect effectV effect effect effect

Age of 2 al.dIj F aI,.dh1l+[, aI. dZ7 l headof Fli dtI [7.- 11z2 family ] L dt I,L hj dt IL, aZ; dt J

All families -0.1487 -0.1474 -0.0013 0.0034 -0.0047 Percentage of total effect -100.0 -99.1 -0.9 -2.3 -3.2 Under 20 - -0.0004 (-0.3) - -0.0002 -0.0009 20-30 - -0.0174 (-11.8) - 0.0057 -0.0003 30-40 - -0.0220 (-14.9) - 0.0144 0.0003 40-50 - -0.0898 (-60.9) - -0.0123 0.0002 50-60 - -0.0144(-9.8) - -0.0040 -0.0018 Over 60 - -0.0034 (-2.3) - -0.0002 -0.0022

- Not applicable. Note: Positive coefficients represent effects which act to increase income inequality; negative coefficients, those which act to reduce income inequality. Source: Calculated from table 5.5. a. The figures in parentheses indicate the percentage composition of the intrasectoral effect. ADDITIONAL REFLECTIONS 263

Table 5.28. Income Disparities, by Sex of Head of Family, 1964 and 1972

Share of Share of Disparity income families in shares Income (percent) (percent) (percentagepoints) relative, Sex of head - of family 1964 1972 1964 1972 19641 1972 1964 1972

Male 93.9 94.1 92.3 93.3 1.6 0.8 1.02 1.01 Female 6.1 5.9 7.7 6.7 -1.6 -0.8 0.79 0.88 All families 100.0 100.0 100.0 100.0 3.2b 1.6b 1.00 1.00

Sources: Same as for table 5.2. a. The ratio of the share of income to the share of families. b. The sum of the absolute values.

Table 5.29. Causes of the Reduction in Income Inequality, by Sex of Head of Family, 1964-72

Intra- Inter- Family Income Total sectoral sectoral weight + disparity effect effecta effect effect effect Sex of r al dI,1 al[ dh, r aLo dZ,1 head of F12 2 _+1 2- family L.i iof dtjJ L ah, dt j X oZ, dt

All families -0.1597 -0.1576 -0.0021 -0 .0007 -0.0014 Percentage of total effect -100.0 -98.7 -1.3 -0.4 -0.9 Male - -0.1561 (-99.0) - -0.0032 -0.0006 Female - -0.0015 (-1.0) - -0.0025 -0.0008

- Not applicable. Note: Positive coefficients represent effects which act to increase income inequality; negative coefficients, those which act to reduce income inequality. Source: Calculated from table 5.6. a. The figures in parentheses indicate the percentage composition of the intrasectoral effect. CHAPTER 6

Taxation and the Inequality of Income and Expenditure

A TYPICAL FAMILY'S TOTAL INCOME [y] is the sum of several income components, such as wage income [w], property income [7r], and transfer income [n]. It also is the sum of various additive expenditure components, such as spending for food and clothing [cl], housing [c21, and education [cD], payments of direct tax [ti] and indirect tax [t2], and savings [s]. Thus: (6.1a) y =w + r + n;

(6.1b) y= C + C2 + C3 + tl + t2 +S. Accordingto equation (6.1b), y is total family income beforetax. If there are n income-receivingfamilies, column vectors can be used to describethe structures of familyincome and expenditure:

(6.2a) Y = Cl + C2 + C3 + T, + T2+ S, where

(6.2b) Y = col (Yi, Y2, .. ),

(6.2c) ci = col (cil c,2, . . . v ci)X (i = 1, 2, 3) (6.2d) T7 = col (til, t., tin), and (i = 1, 2)

(6.2e) S = col (S1, S2, . . . - Thus Y is the structure of family income, Ci is the structure of consumptionof the ith commodity,Ti is the structure of tax payments, and S is the structure of savings. When the family incomestructure [Y] is given, economistscan apply the familiar theory for determiningthe various consumption

264 TAXATION AND THE INEQUALITY OF INCOME AND EXPENDITURE 265 structures [Ci] and tax structures [Ti]. For example, the various consumption structures [Ci] are determined by consumption functions measuring the propensities to consume the commodity ci when y is given; family savings [8] are a residual. The structure of direet tax payments [T1] is related to the structure of total family income [Y] through rates of income tax. The structure of indirect tax payments [T2] is related to the various consumption structures through the rates of sales tax and commodity tax imposed upon various commodities. This chapter is not concerned, however, with the theory for the determination of Ci and Ti. They are assumed to be given and are the points of departure for the analysis here.' Total family income Ey] clearly is the means by which to obtain family welfare; the various consumption categories Eci] and family savings [s] are the ends. The inequality of family income, measured for example by the Gini coefficient [G(Y)], thus is tantamount to the inequality of the means to obtain family welfare. The inequality of family income [G(Y)] is important, then, only because it ultimately leads to the inequality of consumption [G(Ci) l and savings [G(S) ]-the two measures focused upon in this analysis. The structures of family savings [S] and family expenditure on education [C3] respectively represent family investment in physical and human resources. The inequality of these investment patterns in one year, measured by G(S) and G(C3),leads to the inequality of total family income in subsequent years. Thus the inequality of family income persists mainly because the inequality of family investment persists. The inequality of the various family consumption patterns, measured by G(C1) and G(C2), can indicate the economic welfare of families in the narrow sense. In a poor, underdeveloped economy with a consumption standard not far above the subsistence level, the inequality of the consumption of a basic food item corresponds to the inequality of family welfare. In wealthier countries, however, some items are consumed because they are conspicuous. For such items of conspicuous consumption as clothing and housing, a large G(Ci) indicates a sharp distinction in status or among classes. For this reason a large G(Ci) is expected to be positively correlated with G(Y), suggesting that the inequality of total family income

1. The outline of how such deterministic theories might be formulated is discussed at the end of this chapter. 266 TAXATION AND THE INEQUALITY OF INCOME AND EXPENDITURE leads to the inequality of conspicuous consumption. In the present state of knowledge, it is not known whether the designation of a particular commodity as "conspicuous" bears any relation to cultural traits. For purposes of analysis the expenditure on housing [C3 ] has been separated as a special category of consumption. This separation is based on the intuition that housing expenditure in Taiwan is conspicuous insofar as it is more unequal among income-receiving families than expenditure for food and clothing-a hypothesis that can be refuted by the empirical finding that G(C2 ) does not significantly differ from G(C1 ). The inequality of the tax structure, measured by G( T1) and G(T 2), indicates the primary impact of taxation on the inequality of family income. Equation (6.2a) can be rewritten as:

(6.3a) V = Cl + C2 + C3 + S, where family family spending income = on consumer + family spending after goods [ on housing J -tax ii + [family spending family 1 on education Isavings]

(6.3b) V =Y-T 1 --T 2 and family family income income | payments of] [payments ofl after before I[direct tax J Lindirecttax] Ltax -Ltax i

(6.3c) Y = V + T1 + T2 . family 1 family income income + payments of 1 [payments of] before after Ldirect tax J indirect tax J -tax L taxz

In the foregoing equations the column vector V = col (V1 , V2, ... Vn) stands for the structure of family income after tax-that is, for the structure of net income. When the structure and inequality of family income before tax are given, the inequality of the tax structure [G(T ) and G(T 2 )] determines the inequality of income after tax [G(V)]. The relations among G(Y), G(V), and G(Tj) will be indicated more clearly as the analysis unfolds. STATISTICAL DATA 267

In summary, the analysis of the inequality of family expenditure has three purposes: to study the inequality of investment, to study the patterns of consumption, and to study the inequality of taxation -all in relation to their separate impact on the inequality of family income. Having explained the economic significance of this analysis, the discussion now proceeds to introduce the statistical data and the analytical framework. The empirical analysis using this framework will be undertaken in the final two sections.

Statistical Data

The statistical data used in the empirical analysis are for 1964, 1966, 1968, 1970, 1972 and 1973 (see tables 6.5-6.10 in appendix 6.1 at the end of this chapter). Each table presents the following data: the income classes for total family income; the number of families and the total family income for each income class; the expenditure on housing [C2] and education [Ca], the expenditure on all other consumption [cl], the direct tax [t,] and indirect tax [t2j; and the family savings [s]. When the families are grouped into classes, the underlying assumption is that all families within the same class receive the same family income and spend the same amount for each category of consumption.2 The main source for these tables is the DGBAS data, which give a fairly detailed classification of family expenditure. 3 For 1966 the classification contained sixteen major categories as well as detailed subcategories (table 6.1). In all, it had sixty-four items.4 As applied to appendix tables 6.5-6.10, housing expenditure [C2] includes the categories for rent and water charges and for furniture, furnishings, and household equipment; these items are indicated by an asterisk in table 6.1. Educational expenditure [C3] includes

2. The tendency with such a procedure is to underestimate the inequality of all expenditure components that do not have a high positive correlation with the structure of total family income. This difficulty can be avoided only when use is made of the original data-that is, when families are not grouped-rather than published data, which groups families into classes. The original data is in the original DGBAS questionnaires (see the tables appended to chapter four). 3. See appendix 4.1 to chapter four for the sample sizes and other details of the DGBAS data. 4. For different years the DGBAS classifications differ slightly. 268 TAXATION AND THE INEQUALITY OF INCOME AND EXPENDITURE the categories for personal and medical care and for recreation and amusement, as well as the subcategory of miscellaneousconsumption expenditure for education and research; these items are indicated by a double asterisk in table 6.1. Therefore c3 is a proxy for investment in human resources; c2 for conspicuous consumption. Obvi- ously the judgments involved in such definitions of these variables

Table 6.1. Categoriesof HouseholdExpenditure and Their Indirect Tax Burden, 1966

Indirect tax burden Category (percent)

Food 4.10 Beverages and tobacco 42.85 Clothing and other personal effects 5.60 Rent and water charges* 0.54 Rent 0.50 House repairs and installation 0.50 Water charges 1.78 Fuel and light 11.39 Furniture, furnishings, and household equipment* 5.93 Furniture and furnishings 2.41 Textile furnishings 5.60 Appliances for kitchen and bathroom 10.68 Other 10.68 Household operation 3.84 Personal and medical care** 6.59 Personal care n.a. Barber and bath shop services n. a. Medical and health expenses n.a. Transport and communication 7.00 Recreation and amusement** 1.73 Recreation n.a. Books, newspapers, magazines, and stationery n.a. Other n.a. STATISTICAL DATA 269

Table 6. 1 (Continued)

Indirect tax burden Category (percent)

Miscellaneous consumption expenditure 18.59 Financial services n.a. Education and research** n.a. Marriages, birthdays, and funerals n.a. Other n. a. Interest Taxes Household tax House tax Land value tax Land tax Land value improvement tax Land value added tax Inheritance tax Bicycle license tax Income tax Other Gifts and other transfer expenditure Savings

d Indicates items of housing expenditure [c 2 ]. ** Indicates items of educational expenditure [ca]. Not applicable. n.a. Not available. Source: DGBAS, Report on the Survey of Family Income and Expenditure, 1966.

are a priori. For example, the expenditure for fuel and light is ex-

cluded from conspicuous consumption [C2] because it is for cooking. The direct tax [t1 ] in the appendix tables includes all ten items in the category for taxes in table 6.1. In addition to these direct tax payments, families pay indirect tax when consumption expenditures are made. Because the DGBAS data are based on household surveys, the consumption expenditures listed under the various categories in table 6.1 include indirect taxes. A separate procedure was used to estimate the indirect tax payments [t2], which have 270 TAXATION AND THE INEQUALITY OF INCOME AND EXPENDITURE

been subtracted from the DGBAS data to give family consumption expenditures exclusive of indirect tax payments [cl, c2, and c3]. The procedure for this computation is explained in appendix 6.1.

Analytical Framework

It can be seen from equations (6.3a) and (6.3c) that both V and Y are vector sums of a number of components. Thus the inequality of total family income [G( Y) ] and of family income after tax [G( V) ] can be decomposed into factor components according to the following equations 5: (6.4a) G(V) = RIeGc+ RG2 + o3R3G3+ O.R.Gs; inequality of family [effecton effect on income = consumption + housing after expenditure expenditure tax ] [effecon [effecton1 + educational + [ on expenditure] (6.4b) G(Y) = r + OtMG4RtGt± + inequality of family [effect on 1 effect on1 r effect on 1 income = after-tax + o + before ~ [ income [direct tax indirect tax tax Each effect is the product of a weight term [+X], a correlation term [Ril, and a Gini term [GJ. The terms GI, G2, Ga, and G. are the Gini coefficients of the structures of consumption [CJ and savings [S] in equation (6.3a)-that is, GC = G(Ci) and G0 = G(S). Therefore G0 and G. respectively measure the inequality of family investment in human and physical resources. Similarly G, and G, respectively measure the inequality of family expenditure on other consumption and housing consump-

5. The equations are directly obtained by applying equation (10.5) in chapter ten to equations (6.3a) and (6.3c). Notice in equation (6.4) that G(V) = G.. ANALYTICAL FRAMEWORK 271 tion. The terms G1 and G2 respectively measure the inequality of payments by families for direct and indirect tax. The terms RI, R', R', and RS measure the correlation of the vectors C1 , C2, C3, and S with the vector of V. High and positive values of R3 and R. indicate that human and physical investments are heavily concentrated among wealthy families. A high and positive value of R' means that expenditure on housing is very sensitive to the level of total family income and suggests that housing is an item of conspicuous consumption. The terms RD,R', and R' express the correlations of the vectors V, Ti, and T2 with the vector Y. R, would be expected to be close to 1 because any rationally designed tax system should not overtly disturb the rankings of families in the structure of income [Y]- that is, families should have the same rank before and after their tax payments. For a progressive direct tax, R' would be expected to be high and positive, indicating that tax payments become pro- gressively higher as total family income increases. For a regressive indirect tax, R2 would be expected to be negative and close to -1, indicating that the heavier tax burden falls upon low-income families. Equation (6.4b) can be rewritten as: (6.5) G(V) = (1/,BR,)G(Y) - (¶1Rj11/R,)G1- (o2R2/p,B)G2. When the inequality of family income [G (Y)] is given, equation (6.5) shows the impact of taxes on family income after tax. A high and positive R1 , which would be associated with a progressive tax, contributes to the equality of family income after tax. A negative Ri, which would be associated with a regressive tax, contributes to the inequality of family income after tax. The weight terms [¢i] in equations (6.4a) and (6.4b) are defined as follows. Let X be the mean value of any vector X. Then equations (6.3a) and (6.3c) imply that:

(6.6a) V= 01 + 0 2 + C3 + S = - T1 - T 2;

(6.6b) t0 = 01/V, 2 = C2 /'V, C = 0 3 /V, 0. = S/V; and

(6.6c) 4,, = V/Y, 44 = T1 /j, 44 = T2 /V; where (6.6d) + e + is + 4. = 1 and

(6.6e) k 8+ 1 + 02 1. In equation (6.6b) 44 is the consumption expenditure of the ith type expressed as a fraction of total family income excluding taxes; 272 TAXATION AND THE INEQUALITY OF INCOME AND EXPENDITURE

4, is the fraction of average savings in average family income after tax, or the average propensity to save. In equation (6.6c) 0, is the ratio of income after tax to income before, or including, tax; Ot is the total tax payment of the ith type expressed as a fraction of income including tax.

Decomposition of Family Income after Tax

The results of the decomposition according to equation (6.4a) of the Gini coefficientof family income after tax [G(V)] are presented in table 6.2. The time series in this table are graphically represented in figures 6.1-6.4. Figure 6.1 shows the time series of G(V) and that of the four contribution terms [OiRiGi].The once-for-all decline of G(V) indicates that the distribution of family income after tax was generally becoming more equal in this ten-year period. The

Figure 6.1. Contributionsto the Inequality of Family Income after Tax, by Categoryof Expenditure, 1964-73

0.4 Inequality of family income after tax

0.3 -

Consumption expenditure

-< _--.- - __ XI 0.2

Housing expenditure Savings

o.1 ------

0 c - I Educationalexpenditure 0 ~R3G3 1964 1966 1968 1970 1972 1973

Source: Table 6.2. DECOMPOSITION OF FAMILY INCOME AFTER TAX 273

Figure 6.2. Correlation Terms for the Decomposition of Family Income after Tax, by Category of Expenditure, 1964-73

RI Consumption expenditure Educational expenditure R3 1.00 _- _ -

0.98 - \ R2 Housing ' expenditure - * 0.96 _ / R, Savings t 0.94 \ / V 0.92 -

0.90

0 1964 1966 1968 1970 1972 1973

Source: Table 6.2.

expenditure on food, clothing, and other consumer goods accounted for about 50 percent of the inequality of family income after tax [G(V)]; educational expenditure accounted for about 10 percent. Savings and expenditure on housing respectively accounted for 16 percent and 23 percent. The contrast is sharp between the two consumption components. The term for housing expenditure shows an increasing trend; that for other expenditure a decreasing trend. No increasing or decreasing trend could be detected for the two investment components. The difference between them is that the curve for the savings term is mildly U-shaped and that for the education term is inverse U-shaped. In the following discussion the behavior patterns for consumption and investment are separately explained.

Consumption The values of the correlation terms for consumption expenditure [Rc] and housing expenditure [Re] are very close to the unit value (figure 6.2). The higher the family income is after tax, the higher 274 TAXATION AND THE INEQUALITY OF INCOME AND EXPENDITURE

Table 6.2. Decompositionof the Inequality of Family Income after Tax, 1964-73

Item Notation 1964 1966 1968 Shares Other expenditure +1 0.6744 0.6559 0.6478 Housing expenditure 02 0.1211 0.1425 0.1567 Educational expenditure 03 0.0897 0.0924 0.1039 Savings 0.0.1149 0.1092 0.0916 Gini coefficients Other expenditure Gf 0.2598 0.2736 0.2550 Housing expenditure G2 0.3462 0.3481 0.3582 Educational expenditure GC3 0.3587 0.3804 0.3751 Savings Gs 0.7363 0.5908 0.8843 Correlationterms Other expenditure Ro 1.0000 1.0000 0.9945 Housing expenditure R2 0.9948 0.9977 0.9983 Educational expenditure Rc 0.9967 0.9979 0.9979 Savings Rs 0.9921 0.9983 0.9240 Effects Other expenditure . f/4RfGf 0.1752 0.1795 0.1643 Housing expenditure k9RWG2 0.0417 0.0495 0.0560 Educational expenditure OM-G3 0.0321 0.0350 0.0389 Savings -O8R8G. 0.0839 0.0644 0.0748 Compositionof effects (percent) Other expenditure 52.6 54.7 49.2 Housing expenditure 12.5 15.1 16.8 Educational expenditure 9.6 10.7 11.6 Savings 25.3 19.5 22.4 Gini coefficientof income after tax G, 0.3329 0.3284 0.3340

Sources:Calculated from tables 6.5-6.10appended to this chapter. the family expenditure is for both types of consumption. Thus the effect of the variation of the correlation characteristic can be neglected-that is, it can be assumed that Rl and R' are equal to 1- and the analysis can concentrate on 4i and Gi. The share of consumption expenditure [E] exhibits a decreasing trend; the share of housing expenditure [E] an increasing trend DECOMPOSITION OF FAMILY INCOME AFTER TAX 275

1970 1972 1973 Notation Item

Shares 0.6521 0.6150 0.6000 O Other expenditure 0.1407 0.1619 0.1620 42 Housing expenditure 0.1185 0.0870 0.0812 (PC Educational expenditure 0.0887 0.1361 0.1568 0) Savings Gini coefficients 0.2304 0.2343 0.2319 Gi Other expenditure 0.3220 0.3256 0.3534 G2 Housing expenditure 0.3300 0.3299 0.3478 G3 Educhtional expenditure 0.6915 0.5134 0.5335 G, Savings Correiation terms 0.9974 1.0000 1.0000 R' Othet expenditure 1.0000 1.0000 1.0000 R2 Housing expenditure 0.9988 0.9994 0.9994 R3 Educational expenditure 0.9806 1.0000 0.9989 R, Savings Effects 0.1498 0. 1441 0.1391 oIeRGl Other expenditure 0.0453 0.0527 0.0573 2R21G2 Housing expenditure 0.0391 0.0287 0.0282 scRlGc Educational expenditure 0.0601 0.0699 0.0836 O4sR,G. Savings Composition of effects (percent) 50.9 48.8 45.1 Other expenditure 15.4 17.8 18.6 Housing expenditure 13.3 9.7 9.2 Educational expenditure 20.4 23.7 22.1 Savings Gini coefficient of income 0.2943 0.2954 0.3082 G, after tax

(figure 6.3). Because the increase of family income was rapid during this ten-year period, the foregoing trends reveal that the family housing expenditure is income-elastic and other family expenditure is income-inelastic. This pattern is consistent with expectations based on the conventional theory of consumer behavior. The inequality of the distribution of family expenditure on hous- 276 TAXATION AND THE INEQUALITY OF INCOME AND EXPENDITURE

F1igure6.3. Shares for the Decomnpositionof Famnily Income after Tax, by Category of Expenditure, 1964-73

0.7 Consumption expenditure f1 ~~~~~~~~4

0.5

0.3 Housing expenditure Savings

2 _------0.I~~~~~~~~~~~~~~~ 0. 1 C_ =___ _ Educational expenditure 0 1 1 I I 1964 1966 1968 1970 1972 1973

Source: Table 6.2.

ing [G'] was much greater than that of family expenditure on other consumption [EG] (figure 6.4). Thus the expenditure on housing, more than that on other consumer goods, distinguished the class of wealthy families and therefore took on the character of conspicuous consumption. This was true despite the rapid growth of family income over the period. It may be concluded that the difference in the income elasticity of demand for housing and for other consumption expenditure mainly explained the long-run declining trend of 0jRlG, and the long-run increasing trend of O'R'G2 seen in figure 6. 1.

Investment It can be seen from the correlation characteristics in figure 6.2 that educational expenditure and savings were highly correlated with family income after tax. Even the lowest value of R., registered DECOMPOSITION OF FAMILY INCOME AFTER TAX 277

Figure 6.4. Gini Coefficients for the Decomitpositionof Famlily Income after Tax, by Category of Expenditure, 1964-73

0.8 _ G, s / " Savings

N,~~~~ -0.6-

Educational expenditure 0 0.4 - G2 --

Housing expenditure

0.2 Consumption expenditure

O I I I I l I I I I 1964 1966 1968 1970 1972 1973

Source: Table 6.2.

in 1968, is 0.9024. Thus the correlation characteristic can again be neglected, enabling concentration upon 'i and G,.6 The shares of expenditure on education [06] and savings [+8] both present a constant time trend, fluctuating around 10 percent over the ten-year period (see figure 6.3). Families therefore spent about the same percentage of their income on investment in human resources and on physical resources. Notice that the movements of 4. and X4 always are in the opposite direction. When (A.moves up-

6. That all values of Ri in figure 6.2 are close to 1 should come as no surprise. It simply means that wealthier families spent more on each of the items. 278 TAXATION AND THE INEQUALITY OF INCOME AND EXPENDITURE ward, O moves downward, and vice versa. The reason is that when families decide to spend more on education-as they did, for example, before 1970-they saved relatively less. Conversely, when they spent less on education-as they did, for example, after 1970-they saved more. Together the two curves seem to indicate a constant propensity to "save" of about 20 percent up to 1972. In 1973 the sum of i, and 0, increased to 24 percent. It remains to be seen whether this was indicative of a new, increasing trend. Finally the inequality of savings [G8] and the inequality of educational expenditure [Gc] were consistently greater than the inequality of housing expenditure [Gc] and the inequality of consumption expenditure [GO]. Consequently the inequality of family income after tax led more to the inequality of investment (in education or savings) than to the inequality of consumption. The fact that the inequality of investment in one year leads to the inequality of income in subsequent years in part explains the persistence of the inequality of family income over time. It should be observed that the inequality of family saving was much greater than the inequality of family expenditure on education. As pointed out earlier, the percentages of income applied to education and savings were approximately the same at around 10 percent for earlier years (see figure 6.3). Thus the inequality of investment in physical resources is more responsible than the inequality of investment in human resources for the persistent inequality of family income. In arriving at this conclusion, it should be borne in mind that government spends heavily on public education-both on education up to the nine-year level, which became compulsory in 1968, and on higher education. This expenditure is, in principle, very equally distributed among the families benefiting from this policy. The education policy thus has greatly reduced the role of private expenditure on education as a causal factor in contributing to the inequality of family income over time. It should also be noticed that there is a long-run declining trend of G. over time. This means that as family income increases, the low-income families begin to save proportionately more of their income than high-income families. The persistence of such a time trend implies that the inequality of investment in physical resources in the future will contribute less to the inequality of family income than it has in the past. For this reason the distribution of family income in Taiwan can be expected to continue improving. THE IMPACT OF TAXATION ON INCOME INEQUALITY 279

The Impact of Taxation on Income Inequality

The results of the decomposition of the inequality of family income EG(Y)] according to equation (6.4b) appear in table 6.3. The primary purpose of the decomposition is to show whether payments of direct and indirect tax contributed to the equality of family income after tax. The ratio of the Gini coefficient after tax [G.] to the Gini coefficient before tax [G,] shows that there was no significant difference between G. and G, in all the years examined- that is: (6.6) G, _ G,

It can thus be concluded for this ten-year period that the direct impact of taxation on the distribution of family income was neutral and that it brought about neither greater equality nor greater inequality. It follows that the cause of the near-equivalence of G, and G0, in the past should be investigated and that future measures should be introduced so that tax policy can contribute more to the equality of family income. As a first step in this investigation, it should be determined whether the taxation system in Taiwan satisfies certain minimum requirements for being "reasonable."

Is Taiwan's system of taxation reasonable? The impact of taxation is graphically represented by the flow chart in figure 6.5. The income before tax EY = (yr, Y2, y3)] is received by the families [(fl, f2, f3)]; from this income, families make tax payments [T = (tl, t2, t3)] which constitute the structure of the tax burden. That tax burden [T] is the sum of the direct tax burden [T1 = (t1, t4, t,)] and the indirect tax burden [T2 = (t,

2, 3)]. What remains is family income after tax [V = (Vl, V2, V3)]. The near-equivalence of G, and G0,in expression (6.6) implies that the tax burden [T] causes no difference between the degree of inequality in before-tax income [Y] and after-tax income [V]. Thus: (6.7a) Y = V + T, where

(6.7b) T = T, + T2. 280 TAXATION AND THE INEQUALITY OF INCOME AND EXPENDITURE

Table 6.3. Decomposition of the Inequality of Family Income before Tax, 1964-73

Item Notation 1964 1966 1968

Shares Income after tax f 0.9341 0.9277 0.9189 Direct tax f 0.0268 0.0122 0.0139 Indirect tax 2 0.0591 0.0601 0.0672

Gini coefficients Income after tax GD 0.3329 0.3284 0.3340 Direct tax GI 0.4381 0.5208 0.5902 Indirect tax GI 0.2605 0.3229 0.2945

Correlation terms Income after tax R. 0.9988 1.0000 0.9997 Direct tax Rf 0.9781 0.9965 0.9949 Indirect tax R' 0.9724 0.9913 0.9891

Effects Income after tax 0,R,G, 0.3106 0.3047 0.3068 Direct tax 0IRIGGl 0.0029 0.0064 0.0082 Indirect tax 4R4G24 0.0150 0.0192 0.0196

Inequality of income before tax G, 0.3285 0.3303 0.3346

Ratio of inequality of income before tax to that of income after tax G,/IG 1.0133 0.9942 0.9982

Sources: Calculated from tables 6.5-6.10 appended to this chapter.

When total family incomes are arranged in a monotonically nondecreasing order, any rationally designed tax system should satisfy the following conditions:

(6.8a) Y• < Y2 < ... < Yn, which implies that:

(6.8b) V 1 < V2 < ... < V., [no reversal of rank] THE IMPACT OF TAXATION ON INCOME INEQUALITY 281

1970 1972 1973 Notation Item

Shares 0.9234 0.9154 0.9176 ct Income after tax 0.0112 0.0150 0.0146 oi Direct tax 0.0654 0.0695 0.0678 021 Indirect tax

Gini coefficients 0.2943 0.2954 0.3082 GD Income after tax 0.5450 0.5758 0.5830 Of Direct tax 0.2559 0.2423 0.2485 G21 Indirect tax

Correlation terms 1.0000 0.9983 1.0000 R, Income after tax 0.9989 1.0000 1.0000 Rf Direct tax 0.9984 0.9992 1.0000 RI Indirect tax

Effects 0.2718 0.2699 0.2828 ORXG, Income after tax 0.0061 0.0086 0.0085 ti4RfGf Direct tax 0.0167 0.0168 0.0168 021R21G2 Indirect tax

0.2946 0.2953 0.3081 G, Inequality of income before tax

Ratio of inequality of income before tax to that of income 0.9983 1.0003 1.0003 G1/G, after tax

(6.8c) t1< t, < . .. < tn,

fminimum progressiveness [mLnm°f direct tax

(6.8d) t

| minimumprogressiveness I n f total tax 282 TAXATION AND THE INEQUALITY OF INCOME AND EXPENDITURE

Figure 6.5. Flows of Income before Tax to Taxes and Income after Tax, by Family

TI T'TI T 1~~T, tT3 fWVI~~~~~T

T'1 T2

Income before tax (IY,, Y2, Y3) Income after tax = (V,, V2, VS) Total tax = (TI, T2, T3) Direct tax = (TI, T2, TI3) Indirect tax = (TlI, T2', TI3) Source: Constructed by the authors.

The no-reversal-of-rank condition in expression (6.8b) means that the family income rank before tax in expression (6.8a) should not be overtly disturbed by tax payments. In other words, to mini- mize the disincentive effect of taxes, a high-income family should not be taxed so heavily that its after-tax income is lower than the after-tax income of a low-income family. The no-reversal-of-rank condition then means that the tax system should not be too progressive. The conditions of minimum progressiveness in expressions (6.8c) and (6.8d) mean that the tax system should not be too THE IMPACT OF TAXATION ON INCOME INEQUALITY 288 regressive-that is, the higher a family's income, the more it should pay in direct and indirect taxes. Notice that the condition of minimum progressiveness in expression (6.8e) follows from expressions (6.8c) and (6.8d) by equation (6.7b). When the conditions in expressions (6.8b), (6.8c), and (6.8d) are satisfied, the rank correlation is perfect between the vector Y and the vectors V, T1, and T2. Because it follows that the correlation characteristics RV, Rf, and R' then take on unit value, equation (6.4b) assumes the special form7:

(6.9a) R. = R' = R2 = 1 by expression (6.8);

(6.9b) G1 = O,G++ OM+±PGl by equations (6.4b) and (6.9a). The applicability of equation (6.9a) to Taiwan is verified by the values for the correlation terms [Ri] in table 6.3. With the exception of the value of 97 percent observed for 1964, the values of Ri for all other years are very close to the unit value. It can thus be concluded that the taxation system in Taiwan does meet the minimum requirements for being reasonable, at least as defined in equation (6.9a) which gives the conditions for no reversal of rank and minimum progressiveness.

The burden of taxation The system of taxation in Taiwan, although reasonable, was not very progressive during the period under observation because of its neutrality with respect to the distribution of income (see expression [6.6]). To discover the reasons for this to have been so requires analysis of the structure of the tax burden. The decomposition of the index of inequality of the distribution of income [G,] according to equation (6.7a) leads to:

(6.10a) GV = kvRVG.+ TRrTGT, where

(6.10b) OT = k1 + O' and

(6.10c) oi + 02 = 1.

In equation (6.10a) OT is the share of taxes in total income and the sum of the shares of direct and indirect taxes; GT is the Gini coeffi-

7. See the section on correlation characteristics at the end of chapter nine. 284 TAXATION AND THE INEQUALITY OF INCOME AND EXPENDITURE

IF'igure6.6. Contributions to the Inequality of the Tax Burden, 1964-73

Inequality of income before tax

0.3 GInequality of the tax burden

0.2 - Contribution of direct tax Contribution of indirect tax 0.1

OF1964 I 1966 1968 1970 1972 1973I

Source: Table 6.4.

cient of the tax burden. The reasonable properties of the taxation system specified in equation (6.9a) immediately imply that:

(6.1la) G2,= k,G, + OTGT by Rv = RT = 1 from (6.9a) and

(6.11b) G, = (G, - OTGT)/1 . According to equation (6.11b) the total tax burden should, if taxation is to be used as a policy instrument to bring about the equality of the distribution of family income, be unequally distributed and reflected by high values of GT. Because G, is a weighted average of G, and GT, income after tax can be more equally distributed than income before tax if and only if the inequality of taxation is greater than the inequality of income. That is:

(6.12) GV< GY if and only if GT > G, . The neutrality of taxation observed in expression (6.6) implies that the conditions of expression (6.12) were not satisfied. The conditions associated with expression (6.6) and equation (6.11a) immediately show that: (6.13) G, = GV = GT. In other words, the taxation system in Taiwan did not bring about a more equitable distribution of income because the total tax burden was distributed with the same degree of inequality as income before tax. The time paths of GT and G, are shown in figure 6.6. The curve THE IMPACT OF TAXATION ON INCOME INEQUALITY 285 for GCis very close to the curve for GT, and they become closer over time. This verifies the conditions stated in equation (6.13). The equivalence of GCand GT can be analyzed from another angle. Assume a hypothetical marginal tax rate of m: (6.14) dT/dY = m, where m < 1. Whenever the total family income increases by one dollar, the additional total tax payment is m dollars. The average tax rate for all families is given by:

(6.15) rT = (tl + t2 + .. + tn)/(Y1 + Y2 + + Yn) - Under the assumptions of equation (6.14) GT and GC satisfy the following equation8 :

(6.16) GT = (m/OT) GC1 . The equivalence of GT and G, shown in equation (6.13) immediately implies that:

(6.17) m = kT. Equation (6.17) indicates the equivalence of the average and marginal tax rates. This equivalence means that the total tax burden is such that the same percentage of family income is collected as taxes from all families, regardless of their income. Thus, despite the reasonable properties of Taiwan's system of taxation, the overall tax burden was highly regressive according to a modern standard.

Analysis of the burden of taxation The total tax burden is the sum of the direct and indirect tax burdens (see equation [6.7b]). The inequality of the tax burden CGT] is traced in turn to the direct and indirect tax burdens. Apply- ing the decomposition formula to equation (6.7b) gives:

(6.18a) GT = 04RCG1+ O'R,G,, where

(6.18b) +' = 44/4T, 02 = O/4T, and

(6.18c) 4i' + 02 = 1.

8. See theorem 12.2 in chapter twelve. Notice that if the taxation system is reasonable, the value of m must lie between zero and 1-that is, 0 < m < 1. Thus, according to theorem 12.2, the tax payment T corresponds to a type one or type two income when m is a positive fraction. 286 TAXATION AND THE INEQUALITY OF INCOME AND EXPENDITURE

Table 6.4. Decomposition of the Inequality of the Tax Burden, 1964-73

Item Notation 1964 1966 1968

Shares Direct tax 1 0.1031 0.1687 0.1713 Indirect tax 04 0.8968 0.8312 0.8286

Effects Direct tax fGt 0.0451 0.0878 0.1011 Indirect tax 02,G 0.2336 0.2683 0.2440

Composition of effects (percent) Direct tax 16.2 24.7 29.3 Indirect tax 83.8 75.3 70.7

Gini coefficient of tax burden GT 0.2787 0.3561 0.3451

Error term (GT - Gy)/Gy 0.1515 0.0781 0.0313

Sources: Calculated from tables 6.5-6.10 appended to this chapter.

In equation (6.18b) tl and o2 are the percentages of direct and indirect taxes in total taxes. In equation (6.18a) R' and R' are the correlation characteristics of T1 and T2 with T. The reasonable property associated with the expressions of (6.8) implies that9 :

(6.19a) R' = R2 = 1. Hence: (6.19b) GT= 'Gt ±'G2'.+

9. The condition of minimum progressiveness of total tax in expression (6.8e) implies that Y and T have a perfect rank correlation; the conditions of minimum progressiveness of direct and indirect tax in expressions (6.8c) and (6.8d) imply that T, and T2 also have a perfect rank correlation with Y. Therefore T, and T2 have a perfect rank correlationwith T. The economic interpretation is that as a higher incomefamily pays more in total taxes, it also pays more in direct and indirect taxes. THE IMPACT OF TAXATION ON INCOME INEQUALITY 287

1970 1972 1973 Notation Item

Shares 0.1462 0.1775 0.1771 44 Direct tax 0.8537 0.8224 0.8228 42 Indirect tax

Effects 0.0796 0.1022 0.1032 'GC Direct tax 0.2184 0.1992 0.2044 4202 Indirect tax

Composition of effects (percent) 26.7 33.9 33.6 Direct tax 73.3 66.1 66.4 Indirect tax

Gini coefficient 0.2980 0.3014 0.3076 CT of tax burden

0.0115 0.0206 0.0016 (T - GC/CG, Error term

The results of the decomposition of GT according to equation (6.19b) are given in table 6.4. According to equation (6.19b) the values of GT in this table are the sums of the values of 'G/Cand C'Gf.The shares of direct and indirect taxes in the share of total taxes are defined as in equation (6.18b); the values of GCand GCwere taken from table 6.3. The time patterns of these variables are graphically represented in figures 6.6-6.8. Indirect taxes contributed much more than direct taxes to the inequality of taxation [GT] (see figure 6.6). Direct taxes on average accounted for 27 percent of GT; indirect taxes for 73 percent. There nevertheless was a long-run declining trend for the indirect tax contribution and an increasing trend for the direct tax contribution. Thus, although the indirect tax contribution was quantitatively important, that importance relative to the direct tax contribution declined. The two relative tax shares E[4, and 44] maintained a constant time trend over the ten-year period (figure 6.7). The indirect tax share [E4] was much greater than the direct tax share [E4]. The 288 TAXATION AND THE INEQUALITY OF INCOME AND EXPENDITURE

Figure 6.7. Shares for the Decomposition of the Tax Burden, 1964-73

1.0 _

0.8 _ _2

0.6 - Burden of indirect tax

0.4 - Burden of direct tax 0.2 /

1964 1966 1968 1970 1972 1973

Source: Table 6.4.

average value of the indirect tax share was 84 percent; that of the direct tax share 16 percent. Thus the quantitative importance of the indirect tax contribution indicated in figure 6.6 was entirely the result of the importance of indirect tax as a source of government revenue. The burden of indirect tax payments was much more evenly distributed than the burden of the progressive direct tax payments (figure 6.8). Over the ten-year period, the average value of Gf was 0.54; that of G' 0.27. Moreover the inequality of the burden of direct taxes exhibited a long-run increasing trend; that of indirect taxes a long-run declining trend. These patterns conform to those observed in figure 6.6. It can be seen from the foregoing analysis that the canceling of the quantitatively less important and more progressive direct tax payments by the quantitatively more important and regressive indirect tax payments brought about the neutrality of the total tax burden. For tax policy to be an instrument for improving the distribution of income after tax, one practical method is to shift the reliance of government from indirect taxes to direct taxes. The reason is that the progressive features of taxation are built into direct taxes. The curve for the inequality of the indirect tax burden FUTURE RESEARCH 289

Figure 6.8. Gini Coefficients of Direct and Indirect Tax, 1964-73

Direct tax 0.6 -

0.4 G Indirect tax

G2t 0.2

O0 I I I I I I I I 1964 1966 1968 1970 1972 1973

Source: Table 6.4.

[Gf] in figure 6.8 shows a long-run decline-a decline which is not favorable to the equality of income distribution. To reverse this trend the tax rates should be increased for commodities likely to be consumed by families in higher income brackets. In addition to promoting the equality of family income, such a policy would encourage higher saving rates which, in turn, would contribute to economic development.

Future Research

This study of the inequality of family expenditure provides only a partial picture of the inequality of family welfare. There are four reasons for this. First, by concentrating only on the expenditure by families, this study neglects the impact of government expenditure on family welfare. Second, it relies on household surveys for tax data, not on agencies collecting taxes. Third, it does not take full advantage of the household data that is available. Fourth, the method adopted for this study lacks the basis of a positive, deterministic theory. The failure to take government expenditure into account is the major deficiency of this chapter. Family expenditure constitutes only part of the aggregate demand for gross national product. For 290 TAXATION AND THE INEQUALITY OF INCOME AND EXPENDITURE example, the taxes paid by families are spent by government on various programs. Because many families benefit from such public expenditure, the analysis of the inequality of family welfare is incomplete without considering its impact.10 But assigning this expenditure to households, or classes of households, is not easy. The reason is that unemployment compensation or welfare payments to needy families, which could be calculated with relative ease, are not that important in developing countiies. In contrast, public expenditure on health and education is very important. Generally, however, the benefits that families derive from public expenditure must be imputed. Because this expenditure both substitutes and supplements private expenditure in similar categories, it can and should, to the extent possible, be imputed in future studies. Primary data on the administration of government programs for health and education will be needed for this purpose. Because of this study's exclusive reliance on data based upon household surveys, certain issues arose which should be resolved in future research. For one thing, the payments of direct and indirect tax reported by families obviously differ in magnitude from those collected. Moreover the calculation of the indirect tax burden, outlined earlier in this chapter, is only a crude approximation. Satis- factory analysis of the burden of indirect tax, which is quantitatively more important than the burden of direct tax, requires a more adequate framework for the analysis of the shifting incidence of the indirect tax burden in the context of general equilibrium. In addition to data from household surveys, other primary data for the fiscal operations of government will be needed. Despite these requirements for additional data, not even existing data were used to the fullest extent. The wealth of data on family expenditure, such as that detailed in the classification for consumption expenditure in table 6.1, has not been adequately explored. If these data were used more fully, the inequality of family expenditure on consumption could be calculated at a more disaggregated level to provide a firmer grasp of the meaning of the inequality of welfare associated with family consumption. How have these deficiencies affected the results? The failure to incorporate government expenditure probably resulted in an over-

10. There is, moreover, no considerationof hidden taxes, such as those imposed through the rice and fertilizer exchanges. FUTURE RESEARCH 291 estimation of the inequality of family welfare. The failure to incorporate the undistributed profits of corporations and other similar items probably led to an underestimation of the inequality of savings and income. The failure to examine household data at a more disaggregated level of detail probably obscured some underlying trends. Nevertheless a start has been made. The intent here was to show how the basic theory of decomposition presented in this volume might be applied to the inequality of additive expenditure components, just as it was applied to the inequality of additive income components. Finally a word on theory. The method of decomposition used in this chapter basically is empirical. It lacks the foundation of a positive deterministic theory. Therefore one direction for future research into the inequality of expenditure and savings would be to construct a positive deterministic theory based on assumptions about consumer behavior. A theory of this type would not be as difficult to construct, at least conceptually, as that which would apply to some other areas of the analysis of income inequality-for example, to the determination of the inequality of wage income, as posited in chapter four. One possible approach to such a formulation is now discussed. Deterministic theories of the inequality of consumption and taxation are relatively easy to formulate because conventional economic theory has already provided some of the foundations. Abstractly a functional relation is postulated:

(6.20) y = f(x). For example, f(x) represents a consumption function when x stands for income and y stands for consumption. Alternatively f(x) represents a tax function when x stands for income and y stands for tax payments. A special case of equation (6.20) is represented by a linear function:

(6.21) y = b + ax, which represents a linear consumption or other function. To see how equation (6.20) is related to inequality analysis involving patterns in vectors Y = (Yl, Y2, . .. , y.) and X = (xl, x2 , . . .), x) for n families, use the following definition:

DEFINITION 6.1. The vector Y is an f-transformation of X if yi = f (xi) (i = 1, 2, ... ., n). 292 TAXATION AND THE INEQUALITY OF INCOME AND EXPENDITURE

A linear transformation gives the following theorem' 1 :

THEOREM 6.1. GY = (a/s) GD, where 4 = y/. The same language can be used to describe equation (6.21) as a type one, two, or three transformation, depending upon the signs of b and a [see equation (3.7) in chapter three]. When equation (6.21) is interpreted as a consumption function for a particular commodity, a type three commodity (with a < 0) is an "inferior" good. Similarly a type one commodity is a "superior" good, such that the percentage of income spent on this commodity increases with income [see equation (3.13) in chapter three]. In all cases, theorem 6.1 provides information on the inequality of consumption [G,] as related to the inequality of income [EG,] [see equation (3.12) in chapter three]. Precisely the same classification and interpretation can be given when equation (6.21) is interpreted as a tax function: For example, a type three tax is in fact a subsidy which declines with the level of income. When the transformation function (6.20) is nonlinear, theorems similar to 6.1 cannot be readily deduced. For example, for a progressive system of income tax, the transformation function becomes: (6.22a) y = b + tx'/2, with

(6.22b) dY = tx for t > 0, dx when the marginal tax rate [dy/dx] is a linear function of income

Ex]. When the tax payment pattern [Y = (Yl, Y2, ... yj] ), is a transformation of the income pattern [X = (xl, X..., xv)] by equation (6.22a), it is not easy to relate the inequality of the tax burden [G1,] to the inequality of income distribution [G]. The primary reason for this is that the nonlinearity of equation (6.22a) is not amenable to the linearity property of the Gini coefficient. The difficulty, however, is technical rather than conceptual. What needs to be done is to search for another inequality index-one other than the Gini coefficient-that satisfies certain "multiplica- tive" properties. This points the direction future research efforts should probably take to deal with deterministic theories on the problems encountered in this chapter.

11. This theorem was proved as equation (3.12) in chapter three, where a/0 is the elasticity of the linear regression line at the mean point. ESTIMATION OF INDIRECT TAX 293

Appendix 6.1. Estimation of Indirect Tax

The procedure for computing the indirect tax payments of households uses information contained in input-output flow matrices. Let the prices of the n commodities be denoted by the row vector P' = (pi, p2,.. . , pn). Let A = (aij) be the n X n coefficient matrix, and let W' = (wI, W2,. . ., w.) and T' = (t1, t2,. . ., tn) be the values added and indirect tax payments per unit of output for the industries. Then: (6.23) P' = P'A + W' + T', where, for C' = P'A = (ce, C2,. . ., cn), the element ci stands for the intermediary factor cost per unit output of the ith industry. It follows that: (6.24a) P' W'E + T'B, where

(6.24b) B = (I - A)-' is the Leontief inverse matrix. By using the two-industry case as an illustration, the input-output flow table becomes:

Intermediary inputs Final Total Item Industry 1 Industry 2 demand output

Industry 1 ppX,Y plX,2 ply, p,X,

Industry 2 p2X21 p2X22 p 2 Y 2 p2 X 2

Value added w,X, w2X2 Indirect tax T, = tlXI T2 = t2X2

- Not applicable. In the table Xij, Yi, and Xi respectively are interindustry flows, final demand, and total output in physical units. For any base year a monetary input-output flow table contains all the numbers in such cells. Thus the indirect tax rates [ti] are estimated by: (6.25) ti = TilXi = (Ti/Xipi)pi, (i = 1, 2,..., n) where Ti and Xipi are the marginal entries in the table. If the unit of measurement for output is normalized so that pi = 1, then equation 294 TAXATION AND THE INEQUALITY OF INCOME AND EXPENDITURE

(6.25) reduces to: (6.26) ti = TilXipi, (i = 1, 2,..., n) which can be estimated from the marginal entries. The rates of tax burden, given by (b6, b 2 ,..., bn), are defined by having bi be the amount of indirect tax payment for every dollar spent on the ith commodity or, equivalently, for every normalized unit of commodity purchased. Thus:

(6.27) bi = t,. (i = 1, 2,..., n) This procedure of estimation is based on the assumption that all purchasers of a commodity pay the indirect taxes-that is, all indirect tax burdens are shifted to the consuming public. By using input-output tables for 1966, the average values of the indirect tax burden [(b1, b2,. . ., b,)] were calculated for the various consumption categories.12 The rates of tax burden were revised whenever input-output tables were available for years other than 1966. These rates were then applied to the DGBAs data for the various categories of family consumption to obtain the structure of indirect tax payments given in tables 6.5-6.10, beginning on page 296.

12. Economic Planning Council, Interregional Input-Output Tables, Taiwan Area Republic of China, 1966. (Taipei, n.d.).

296 TAXATION AND THE INEQUALITY OF INCOME AND EXPENDITURE

Table 6.5. Family Income and Expenditure, by Category and Income Class, 1964 (thousands of N.T. dollars) Number of Total family All other Housing Income class families income expenditure expenditure (N.T. dollars) [N] [Yd] [C1] [02] Lessthan 6,000 22,288 97,612 74,206 12,938 6,000-8,000 45,294 318,829 247,062 39,524 8,000-10,000 51,046 458,795 365,144 54,750 10,000-12,000 86,994 955,018 794,188 107,260 12,000-14,000 113,596 1,471,883 1,117,165 160,293 14,000-16,000 130,132 1,960,103 1,492,311 200,924 16,000-18,000 132,289 2,244,952 1,556,775 241,157 18,000-20,000 140,916 2,664,356 1,937,333 237,670 20,000-22,000 153,857 3,226,015 2,343,125 346,986 22,000-24,000 144,511 3,325,103 2,243,790 372,368 24,000-26,000 127,975 3,194,728 2,206,247 341,771 26,000-28,000 140,916 3,793,958 2,511,383 451,987 28,000-30,000 105,687 3,061,453 2,084,927 354,635 30,000-32,000 79,805 2,469,080 1,614,334 280,026 32,000-34,000 78,367 2,586,469 1,699,524 320,036 34,000-36,000 76,210 2,664,522 1,681,692 285,621 36,000-38,000 63,268 2,335,582 1,473,956 242,951 38,000-40,000 43,138 1,684,054 1,032,257 223,682 40,000-45,000 100,654 4,248,315 2,625,497 504,021 45,000-50,000 73,334 3,467,577 1,976,334 400,296 50,000-55,000 50,327 2,631,650 1,510,906 365,021 55,000-60,000 44,576 2,558,480 1,470,207 295,625 60,000-65,000 30,915 1,930,572 1,027,877 233,646 65,000-70,000 21,569 1,447,266 763,400 201,672 70,000-75,000 17,255 1,242,817 658,269 189,453 75,000-80,000 13,660 1,054,572 604,423 127,617 80,000-90,000 20,131 1,687,238 902,263 191,357 90,000-100,000 13,660 1,293,438 646,044 79,978 100,000-150,000 23,006 2,819,096 1,319,552 316,022 150,000-200,000 4,314 722,397 359,226 77,929 200,000-300,000 1,438 345,660 123,723 11,186 More than 300,000 719 394,943 77,529 9,256

Total income 2,151,847 64,356,533 40,540,669 7,277,658

Source: DGBAs, Report on the Survey of Family Income and Expenditure, 1964. ESTIMATION OF INDIRECT TAX 297

Educational expenditure Direct tax Indirect tax Savings Income class [C3] [T1] [T2] [S] (N.T. dollars) 7,340 522 8,489 -5,883 Less than 6,000 24,954 1,033 24,921 - 18,665 6,000-8,000 31,370 1,745 45,146 -39,360 8,000-10,000 66,647 3,860 67,929 -84,866 10,000-12,000 102,587 6,640 92,862 -7,664 12,000-14,000 137,658 11,277 121,694 -3,761 14,000-16,000 156,026 15,033 227,912 48,049 16,000-18,000 203,476 12,824 168,031 105,022 18,000-20,000 245,260 25,023 208,803 56,818 20,000-22,000 231,470 19,681 200,723 257,071 22,000-24,000 297,754 15,394 196,947 136,615 24,000-26,000 353,339 15,990 232,621 228,638 26,000-28,000 276,981 19,153 188,234 137,523 28,000-30,000 253,947 13,564 147,725 159,484 30,000-32,000 228,298 16,115 156,895 165,601 32,000-34,000 217,505 15,376 157,477 306,851 34,000--36,000 203,499 13,169 144,727 257,280 36,000-38,000 139,284 10,824 92,619 185,388 38,000-40,000 320,786 24,945 243,601 529,465 40,000-45,000 320,217 28,094 182,970 559,666 45,000-50,000 240,236 29,174 139,923 346,390 50,000-55,000 243,711 22,161 138,547 388,229 55,000-60,000 192,855 9,316 100,311 366,567 60,000-65,000 149,340 8,538 79,668 244,648 65,000-70,000 122,918 15,420 63,072 193,685 70,000-75,000 83,144 4,550 59,945 174,893 75,000-80,000 137,731 18,447 82,962 354,478 80,000-90,000 126,150 13,805 61,651 365,810 90,000-100,000 179,539 38,199 113,025 852,759 100,000-150,000 66,048 4,529 33,494 181,171 150,000-200,000 15,329 936 14,192 180,294 200,000-300,000 15,088 91 6,456 286,523 More than 300,000 5,390,487 435,428 3,803,572 6,908,719 Total income 298 TAXATION AND THE INEQUALITY OF INCOME AND EXPENDITURE

Table 6.6. Family Income and Expenditure, by Category and Income Class, 1966 (thousands of N.T. dollars)

Number of Total family All other Housing Income class families income expenditure expenditure (N.T. dollars) [N] [Yi] [C1] [C2]

Less than 6,000 13,044 62,367 45,999 7,924 6,000-8,000 36,228 273,539 197,469 34,811 8,000-10,000 54,624 533,261 377,014 68,484 10,000-12,000 61,417 710,762 516,788 84,344 12,000-14,000 109,990 1,505,136 1,058,954 175,794 14,000-16,000 112,595 1,761,244 1,222,373 212,237 16,000-18,000 131,632 2,321,090 1,607,048 274,464 18,000-20,000 141,767 2,799,545 1,964,355 340,322 20,000-22,000 165,090 3,570,040 2,421,485 434,864 22,000-24,000 137,202 3,254,517 2,153,717 459,149 24,000-26,000 138,421 3,511,997 2,349,874 466,070 26,000-28,000 122,909 3,407,384 2,212,159 467,090 28,000-30,000 125,897 3,693,025 2,432,312 449,887 30,000-32,000 101,761 3,228,045 2,081,560 428,139 32,000-34,000 81,221 2,732,158 1,712,836 358,813 34,000-36,000 75,132 2,671,424 1,726,170 344,376 36,000-38,000 73,454 2,770,170 1,707,057 401,896 38,000-40,000 55,910 2,194,434 1,330,121 302,788 40,000-45,000 118,578 5,214,635 3,145,169 710,392 45,000-50,000 84,411 4,135,582 2,432,101 556,068 50,000-55,000 73,255 3,958,065 2,326,276 549,979 55,000-60,000 56,536 3,328,065 1,904,726 523,617 60,000-65,000 49,381 3,145,084 1,792,069 455,654 65,000-70,000 27,181 1,861,423 939,498 258,880 70,000-75,000 23,948 1,774,913 1,021,464 191,537 75,000-80,000 18,563 1,464,804 763,174 195,764 80,000-90,000 26,928 2,358,611 1,167,754 311,798 90,000-100,000 16,646 1,640,462 805,344 266,784 100,000-150,000 33,140 3,943,986 1,908,467 474,443 150,000-200,000 9,833 1,711,977 750,419 189,974 More than 200,000 4,341 957,819 457,922 116,412

Total income 2,281,035 76,495,564 46,549,674 10,112,754

Source: DGBAS, Report on the Survey of Family Income and Expenditure, 1966. ESTIMATION OF INDIRECT TAX 299

Educational expenditure Direct tax Indirect tax Savings Income class [C3I [T1] [T,] IS] (N.T. dollars)

3,849 817 3,536 242 Less than 6,000 20,401 669 14,122 6,067 6,000-8,000 34,570 2,861 35,335 14,997 8,000-10,000 50,756 5,482 46,193 7,199 10,000-12,000 104,107 11,253 93,755 61,273 12,000-14,000 121,609 13,860 106,626 84,539 14,000-16,000 163,236 16,630 137,731 121,981 16,000-18,000 204,125 20,184 165,739 104,820 18,000-20,000 268,183 27,898 218,141 199,469 20,000-22,000 244,487 27,596 185,825 183,743 22,000-24,000 264,690 25,475 205,756 200,132 24,000-26,000 260,988 27,035 201,686 238,426 26,000-28,000 303,707 36,810 221,112 249,197 28,000-30,000 284,319 25,316 196,888 211,823 30,000-32,000 224,592 21,328 223,391 191,198 32,000-34,000 242,185 28,019 162,461 168,213 34,000-36,000 269,747 27,251 170,517 193,702 36,000-38,000 179,888 30,077 133,288 218,272 38,000-40,000 514,604 64,918 317,467 462,085 40,000-45,000 432,182 59,208 258,465 394,558 45,000-50,000 369,419 54,757 230,930 426,704 50,000-55,000 312,544 33,614 206,249 347,315 55,000-60,000 325,390 36,066 197,792 338,113 60,000-65,000 169,672 24,776 107,799 360,798 65,000-70,000 200,324 25,797 112,163 223,628 70,000-75,000 109,913 18,154 85,716 292,083 75,000-80,000 227,136 49,345 131,922 470,656 80,000-90,000 140,639 36,321 92,269 299,105 90,000-100,000 313,797 87,404 207,176 952,699 100,000-150,000 100,353 45,234 78,058 547,939 150,000-200,000 94,423 49,033 46,328 175,701 More than 200,000

6,558,835 933,188 4,594,436 7,746,677 Total income 800 TAXATION AND THE INEQUALITY OF INCOME AND EXPENDITURE

Table 6.7. Family Income and Expenditure, by Category and Income Class, 1968 (thousandsof N.T. dollars) Number of Totalfamily All other Housing Income class families income expenditure expenditure (N.T. dollars) [N] [YI] [C1] [C2] Less than 6,000 8,717 35,623 54,197 9,683 6,000-8,000 11,883 84,843 59,334 11,651 8,000-10,000 24,464 216,705 145,623 42,804 10,000-12,000 48,397 543,308 366,065 83,187 12,000-14,000 40,271 528,317 370,345 74,419 14,000-16,000 72,769 1,103,666 789,980 152,426 16,000-18,000 103,715 1,806,929 1,275,112 242,767 18,000-20,000 119,195 2,290,129 1,733,917 299,601 20,000-22,000 123,418 2,605,688 1,853,384 319,900 22,000-24,000 112,758 2,603,833 1,792,427 296,260 24,000-26,000 134,010 3,386,270 2,364,914 445,470 26,000-28,000 106,404 2,875,279 1,904,022 354,415 28,000-30,000 128,242 3,751,380 2,510,261 538,790 30,000-32,000 133,719 4,192,962 3,284,440 542,595 32,000-34,000 87,112 2,881,135 1,820,324 469,365 34,000-36,000 89,516 3,148,092 2,022,361 454,944 36,000-38,000 79,764 2,966,426 1,851,886 397,883 38,000-40,000 79,784 3,126,891 1,937,608 435,450 40,000-45,000 168,012 7,243,895 4,677,913 1,055,272 45,000-50,000 152,750 7,244,441 4,491,360 1,067,183 50,000-55,000 125,936 6,651,426 3,798,543 995,421 55,000-60,000 81,178 4,692,924 2,675,855 768,522 60,000-65,000 69,395 4,367,069 2,404,218 695,035 65,000-70,000 53,806 3,636,707 1,987,697 613,914 70,000-75,000 42,780 3,096,804 1,798,128 517,994 75,000-80,000 27,902 2,164,001 1,150,017 344,747 80,000-90,000 42,728 3,760,734 1,880,158 585,319 90,000-100,000 32,712 3,078,102 1,673,003 430,228 100,000-150,000 41,821 5,318,524 2,264,500 803,367 150,000-200,000 14,725 2,549,714 1,078,425 375,230 200,000-300,000 10,902 2,835,251 1,051,300 376,549 More than 300,000 3,831 1,581,337 296,235 79,433

Total income 2,372,616 96,368,405 57,363,552 13,879,824 Source: DGBAS, Reporton the Surveyof FamilyIncome and Ezpenditure,1968. ESTIMATION OF INDIRECT TAX 301

Educational expenditure Direct tax Indirect tax Savings Income class [C3] [T1] [T21 [S] (N.T. dollars) 3,783 248 4,682 -36,971 Less than 6,000 7,360 584 6,529 -615 6,000-8,000 12,643 505 15,628 -498 8,000-10,000 42,658 3,119 43,213 5,066 10,000-12,000 41,352 3,873 38,978 -650 12,000-14,000 86,052 5,022 82,809 -12,623 14,000-16,000 135,314 12,142 134,300 7,294 16,000-18,000 175,764 14,610 135,355 -69,188 18,000-20,000 233,165 14,958 191,661 -7,380 20,000-22,000 234,553 16,316 196,667 67,610 22,000-24,000 313,122 26,028 237,262 -526 24,000-26,000 219,181 18,214 197,124 182,323 26,000-28,000 326,565 25,314 263,808 86,642 28,000-30,000 356,717 29,728 389,915 -410,433 30,000-32,000 259,031 26,435 196,544 109,436 32,000-34,000 274,268 28,058 212,945 155,516 34,000-36,000 251,795 15,843 198,418 250,601 36,000-38,000 322,405 32,569 217,924 180,935 38,000-40,000 720,730 77,721 550,087 162,172 40,000-45,000 812,897 91,705 500,460 280,836 45,000-50,000 669,678 100,345 433,001 654,438 50,000-55,000 454,778 81,903 309,853 402,013 55,000-60,000 447,287 55,957 277,947 486,625 60,000-65,000 316,821 45,940 232,206 440,129 65,000-70,000 345,589 47,558 203,802 183,733 70,000-75,000 257,627 21,915 140,840 248,855 75,000-80,000 381,971 90,996 212,303 609,987 80,000-90,000 326,565 76,994 195,231 376,081 90,000-100,000 458,436 117,656 368,717 1,305,848 100,000-150,000 287,372 73,831 117,593 617,263 150,000-200,000 239,649 67,047 114,502 986,204 200,000-300,000 185,709 119,976 53,458 846,527 More than 300,000 9,200,837 1,343,110 6,473,762 8,107,320 Total income 302 TAXATION AND THE INEQIUALITY OF INCOME AND EXPENDITURE

Table 6.8. Family Income and Expenditure, by Category and Income Class, 1970 (thousandsof N.T. dollars) Number of Totalfamily All other Housing Income class families income expenditure expenditure (N.T. dollars) [NJ [YN [CI] [C2]

Less than 6,000 5,072 - 12,852 49,797 8,163 6,000-8,000 13,354 95,173 76,922 15,128 8,000-10,000 11,012 96,943 83,258 14,865 10,000-12,000 14,763 163,810 105,736 22,203 12,000-14,000 26,796 351,231 259,537 45,215 14,000-16,000 41,593 622,151 427,667 79,408 16,000-18,000 50,611 857,590 630,763 92,926 18,000-20,000 64,726 1,225,430 896,503 131,563 20,000-22,000 76,780 1,619,145 1,252,162 194,703 22,000-24,000 67,784 1,560,938 1,380,001 189,467 24,000-26,000 106,759 2,666,382 1,819,552 324,928 26,000-28,000 110,679 2,986,573 1,996,355 341,263 28,000-30,000 96,886 2,798,284 1,859,128 328,274 30,000-32,000 106,133 3,290,549 2,147,211 377,167 32,000-34,000 105,405 3,479,122 2,252,726 415,203 34,000-36,000 105,273 3,686,013 2,417,061 417,609 36,000-38,000 124,543 4,592,604 2,911,929 588,941 38,000-40,000 91,980 3,579,819 2,309,551 462,964 40,000-45,000 205,860 8,707,838 5,442,467 1,128,665 45,000-50,000 181,317 8,564,914 5,264,774 1,117,375 50,000-55,000 118,746 6,221,924 3,728,342 846,048 55,000-60,000 106,340 6,096,172 3,500,004 833,203 60,000-65,000 89,350 5,559,718 3,144,018 811,549 65,000-70,000 69,658 4,688,358 2,566,119 678,630 70,000-75,000 48,114 3,486,654 1,933,123 517,292 75,000-80,000 33,838 2,620,015 1,410,393 356,708 80,000-90,000 44,887 3,794,328 2,088,656 535,956 90,000-100,000 42,926 4,050,229 2,165,341 566,552 100,000-150,000 56,607 6,670,916 3,348,734 814,693 150,000-200,000 18,849 3,132,936 1,470,198 444,447 200,000-300,000 7,032 1,636,277 655,435 143,279 More than 300,000 731 256,802 112,018 35,818 Total income 2,244,404 99,145,986 59,705,481 12,880,205

Source:DG3AS, Reporton the Surveyof Family Incomeand Expenditure,1970. ESTIMATION OF INDIRECT TAX 0S0

Educational expenditure Direct tax Indirect tax Savings Income class [Cal [T,] [T2] [S] (N.T. dollars)

10,286 630 4,581 -86,309 Less than 6,000 13,793 484 6,415 - 17,569 6,000-8,000 10,007 518 7,598 - 19,303 8,000-10,000 14,176 578 13,254 7,863 10,000-12,000 29,495 1,432 32,809 - 17,257 12,000-14,000 84,065 3,656 46,702 -19,347 14,000-16,000 70,077 3,555 68,627 - 8,358 16,000-18,000 108,784 7,046 67,150 14,384 18,000-20,000 134,379 8,717 115,912 -86,728 20,000-22,000 142,500 10,633 108,313 -269,976 22,000-24,000 254,516 10,143 191,926 65,317 24,000-26,000 284,275 17,310 210,269 137,101 26,000-28,000 290,619 15,191 197,540 107,532 28,000-30,000 296,876 17,255 223,875 228,165 30,000-32,000 367,080 22,297 242,746 179,070 32,000-34,000 392,666 23,438 261,728 173,511 34,000-36,000 455,356 24,614 308,055 303,709 36,000-38,000 405,405 30,559 237,839 133,501 38,000-40,000 933,292 70,214 609,660 523,540 40,000-45,000 958,163 75,199 582,127 567,276 45,000-50,000 729,562 50,299 411,696 455,977 50,000-55,000 716,513 60,621 400,311 585,520 55,000-60,000 681,695 74,324 360,647 487,485 60,000-65,000 569,761 73,659 297,041 503,148 65,000-70,000 409,049 42,954 221,380 362,856 70,000-75,000 325,179 44,690 173,506 309,539 75,000-80,000 464,104 53,525 243,317 408,770 80,000-90,000 475,541 71,795 258,012 512,983 90,000-100,000 701,009 174,798 282,320 1,349,362 100,000-150,000 307,215 72,385 187,506 651,185 150,000-200,000 176,982 34,843 94,094 531,644 200,000-300,000 37,841 12,424 15,007 43,694 More than 300,000 10,850,261 1,109,786 6,481,963 8,118,290 Total income 304 TAXATION AND THE INEQUALITY OF INCOME AND EXPENDITURE

Table 6.9. Family Income and Expenditure, by Category and Income Class, 1972 (thousandsof N.T. dollars) Number of Total family All other Housing Income class families income expenditure expenditure

(N.T. dollars) [N] [Yd] [C1] [C2 ]

Less than 10,000 11,418 93,232 58,129 16,820 10,000-15,000 24,575 314,301 207,526 46,255 15,000-20,000 63,724 1,128,238 778,304 142,963 20,000-25,000 106,913 2,443,578 1,615,347 313,822 25,000-30,000 157,288 4,312,587 2,886,558 562,800 30,000-35,000 216,839 7,044,936 4,653,777 924,673 35,000-40,000 248,665 9,371,680 5,990,899 1,256,042 40,000-45,000 252,387 10,720,908 6,735,904 1,509,213 45,000-50,000 248,324 11,790,427 7,246,380 1,689,363 50,000-55,000 200,652 10,555,480 6,360,216 1,523,170 55,000-60,000 186,462 10,721,843 6,359,583 1,515,719 60,000-65,000 148,420 9,271,515 5,415,123 1,412,963 65,000-70,000 136,792 9,215,939 5,291,237 1,374,419 70,000-75,000 122,339 8,838,724 5,008,457 1,397,870 75,000-80,000 94,762 7,332,131 4,104,498 1,117,977 80,000-85,000 76,330 6,303,236 3,381,900 966,197 85,000-90,000 68,550 6,003,608 3,262,912 883,129 90,000-95,000 55,417 5,109,051 2,645,938 841,060 95,000-100,000 36,458 3,554,360 1,821,546 554,000 100,000-150,000 236,255 27,872,800 14,163,585 4,552,994 150,000-200,000 52,057 8,879,408 3,843,180 1,400,525 200,000-300,000 21,966 5,076,387 1,902,820 635,211 More than 300,000 4,864 1,746,755 674,682 220,433

Total income 2,771,457 167,701,124 94,408,501 24,857,618

Source:DGBAS, Reporton the Surveyof FamilyIncome and Expenditure,1972. ESTIMATION OF INDIRECT TAX 805

Educational expenditure Direct tax Indirect tax Savings Income class [C3] [TI] [T2] [S] (N.T. dollars)

7,026 173 5,906 5,178 Less than 10,000 21,176 1,142 27,758 10,444 10,000-15,000 81,909 3,487 93,935 27,640 15,000-20,000 162,080 9,157 196,920 146,252 20,000-25,000 305,916 20,589 340,636 196,088 25,000-30,000 466,922 35,873 543,905 419,786 30,000-35,000 677,383 48,909 717,500 680,947 35,000-40,000 745,254 77,828 812,416 840,293 40,000-45,000 894,649 91,681 879,792 988,562 45,000-50,000 864,473 103,121 834,234 870,266 50,000-55,000 888,558 123,214 773,020 1,061,749 55,000-60,000 701,356 118,086 661,359 962,628 60,000-65,000 753,610 118,826 658,866 1,018,981 65,000-70,000 721,286 112,321 619,651 979,139 70,000-75,000 621,313 92,842 529,684 865,817 75,000-80,000 561,288 96,570 420,132 877,149 80,000-85,000 554,572 94,819 412,853 795,323 85,000-90,000 448,308 98,609 338,819 736,317 90,000-95,000 326,160 66,582 245,080 540,992 95,000-100,000 2,393,664 655,079 1,748,797 4,358,681 100,000-150,000 685,128 285,057 495,164 2,170,354 150,000-200,000 357,276 158,975 225,048 1,797,057 200,000-300,000 123,588 110,673 74,946 542,433 More than 300,000

13,362,895 2,523,613 11,656,421 20,892,076 Total income 306 TAXATION AND THE INEQUALITY OF INCOME AND EXPENDITURE

Table 6.10. Family Income and Expenditure, by Category and Income Class, 1973 (thousands of N.T. dollars) Number of Totalfamily All other Housing Income class families income expenditure expenditure (N.T. dollars) [N] [Yd [CI] [C2]

Lessthan 10,000 4,706 32,729 43,155 7,396 10,000-15,000 13,142 173,702 177,907 33,372 15,000-20,000 33,413 601,385 453,219 93,377 20,000-25,000 63,584 1,447,121 981,868 181,356 25,000-30,000 93,436 2,579,618 1,713,159 310,933 30,000-35,000 147,877 4,789,163 3,262,488 579,117 35,000-40,000 187,831 7,061,009 4,485,162 872,249 40,000-45,000 178,633 7,591,085 4,904,235 978,339 45,000-50,000 228,614 10,845,636 6,885,053 1,410,873 50,000-55,000 202,529 10,634,583 6,796,902 1,420,303 55,000-60,000 185,412 10,645,307 6,578,248 1,467,923 60,000-65,000 185,849 11,572,819 7,158,236 1,587,324 65,000-70,000 157,879 10,606,557 6,284,235 1,537,840 70,000-75,000 142,171 10,291,020 5,992,513 1,536,800 75,000-80,000 125,281 9,703,135 5,604,665 1,432,037 80,000-85,000 109,654 9,039,353 5,171,099 1,485,437 85,000-90,000 104,333 9,110,737 5,134,329 1,385,537 90,000-95,000 77,403 7,141,273 3,975,464 1,075,972 95,000-100,000 68,908 6,701,063 3,619,996 1,039,971 100,000-150,000 383,675 45,830,233 23,269,023 7,566,972 150,000-200,000 98,356 16,631,725 7,470,937 2,763,891 200,000-300,000 45,401 11,113,270 4,350,321 1,746,133 More than 300,000 20,425 8,997,359 3,024,034 1,162,432

Total income 2,858,512 213,140,882 117,336,248 31,675,584

Source: DGBAs, Report on the Survey of Family Income and Expenditure, 1973. ESTIMATION OF INDIRECT TAX 307

Educational expenditure Direct tax Indirect tax Savings Income class [CW] [Tl] [T2] [S] (N.T. dollars)

1,881 251 7,368 -27,322 Less than 10,000 24,357 1,119 19,208 -82,261 10,000-15,000 55,311 2,445 53,914 56,881 15,000-20,000 94,660 6,286 118,565 64,386 20,000-25,000 144,763 12,082 214,482 184,199 25,000-30,000 300,236 20,666 376,728 249,928 30,000-35,000 431,468 39,025 557,565 675,540 35,000-40,000 514,269 39,233 573,203 581,806 40,000-45,000 696,253 65,314 794,873 993,270 45,000-50,000 679,973 77,628 784,418 875,359 50,000-55,000 716,455 79,408 773,263 1,030,010 55,000-60,000 813,520 87,733 861,387 1,064,619 60,000-65,000 822,757 100,674 783,415 1,077,636 65,000-70,000 772,428 120,361 728,338 1,140,580 70,000-75,000 766,824 106,504 707,480 1,086,625 75,000-80,000 646,411 123,319 627,028 986,059 80,000-85,000 735,645 125,243 634,321 1,095,662 85,000-90,000 553,968 99,321 494,723 828,825 90,000-95,000 616,227 99,808 475,210 849,851 95,000-100,000 3,835,007 811,851 2,982,699 7,364,681 100,000-150,000 1,382,955 427,850 995,448 3,590,643 150,000-200,000 807,556 285,697 549,114 3,374,448 200,000-300,000 475,088 390,255 337,190 3,608,360 More than 300,000

15,880,012 3,122,073 14,449,940 30,669,025 Total income CHAPTER 7

Relevanceof Findings for Policy

THE ULTIMATE PURPOSE of the examination of Taiwan's development experience, indeed any country's development experience, should be more than simply attempting to understand what happened during a specified period. It should be to distill conclusions that may be relevant to other developing societies and to determine special features that are likely to be irrelevant elsewhere. We consequently have tried to illuminate the possibilities, at various levels of aggregation and analysis, for minimizing the conflict between growth and equity. Readers may nevertheless expect a listing of policy recommendations that stem from such an analysis. Thus, even where our work is preliminary and tentative, which it generally is, we will at least indicate the kinds of policy conclusions that seem to be supported by the empirical findings. Before proceeding to such a listing, however, two general pre- cautions are necessary. One has to do with the extent to which policy is based on sound theory or on a combination of vaguely conceived relations and good intentions. The other has to do with the extent to which analysis of the distribution of income is purely economic or intertwined with other disciplines. Postwar growth has been associated with the observed general worsening of the distribution of income in most developing countries. This pattern has elicited strong protests: "Growth has failed. Governments must resort to direct, even radical actions to correct the situation." The actions proposed usually include land and fiscal reform, public works programs, and major packages of poverty relief and welfare. But what is the basis for the contention that the primary strategy of growth has failed and that direct intervention

308 RELEVANCE OF FINDINGS FOR POLICY 309

is required to fix up FID after the fact? All too frequently the evidence is little more than a crude correlation between high rates of growth and worsening indexes of income inequality. It is easy to sympathize with the humanitarian instincts, and to honor the political instincts, that propel observers to the conclusion that radical change is required. But the general absence of underlying positive analysis is open to question. Consider medicine. After many years of basic research and the accumulation of substantial knowledge, a sure cure for cancer still has not been found. Yet few experts favor declaring a "war on cancer" if that means abandoning a step-by-step scientific approach to the problem. Similarly it would be unwise to reject the basic accumulated tool kit of economics, to claim that growth does not work without specifying alternative growth paths, or to raise false hopes by stating that a "quick fix" is possible and has been worked out analytically. To do any of these things would probably impede the cause, not advance it. Accumulated economic theory must provide a framework that enables economists and planners to differentiate the relevant from the irrelevant and to rule out logical absurdities. Such a framework, to be achieved through the traditional mixture of deductive and inductive analysis, is a prerequisite for understanding the relations between distribution and growth-and thus for knowing what to do about them. True, such a framework is only now beginning to emerge. Although still inadequate, it is the best we have, and it can be improved in the future. The policy implications listed in this chapter should therefore be interpreted in this context. They have been developed within the limits of existing theory and method, and much additional work is required to corroborate or refute them. A second general precaution is related to the realization that a society's modernization involves, in addition to economic elements, important noneconomic elements relevant to the problem at hand. For example, inductive evidence and deductive logic may indicate that institutional discrimination against women in the labor force is relevant to wage income inequality (see chapter four). Although this finding may decidedly be relevant to policy, we find it difficult, as economists, to go beyond the stylized prescription that such discrimination should be removed, and we leave to others the task of designing an appropriate action program. In fact, policies relevant to the family distribution of income seldom are purely economic. Many interdisciplinary complexities relate to such issues as nepotism, family formation, and imperfections in educational 310 RELEVANCE OF FINDINGS FOR POLICY access. If some of the policy conclusions cited below seem terse and barren, the excuse is that we have followed a natural tendency to appeal to a division of labor among social scientists. Here, as elsewhere, good policy should be based on good theory. The analysis of determinants of the family distribution of income still is at an early, largely inductive, and pretheoretical stage. In the introduction we tried to explain the overall framework of reasoning adopted to guide the work of this volume. Our findings and their relevance for policy are presented following the same pattern. At the aggregate level, the most important, if general, policy conclusion which may be derived from our work is this: * It is possible for economic growth to be compatible with an improved distribution of income during every phase of the transition from colonialism to modern growth. Taiwan's experience demonstrates that if assets are not distributed too unequally, a growth path initially based on a flexible version of primary import substitution, followed by the timely reduction of the veil between a changing endowment and relative factor and commodity prices, can yield this result. True, few other developing countries have the same combination of a relatively favorable initial distribution of assets and a willingness to deploy the market mechanism effectively over time. But the experience in Taiwan does not support those who argue that because tinkering with relative prices did not work in the 1950s and 1960s, we must now reach for the radical medicine bottle. Nor does it support the argument that the market solution at every step of the way will, in the presence of powerful landed or industrial interests, yield the desired complementarity between the objectives of growth and equity. What it does support is the conclusion that, given initial conditions that are not too unfavorable, such complementarity can be achieved by affecting the basic growth path, not by following what may be called a secondary or mop-up strategy through direct interventions by government. That is, such complementarity can be achieved by following a different primary strategy of transition growth. The basic thesis of this volume then is that an equitable level of FID can come about mainly through the kind of economic growth which is generated and hence that FID policy should center on growth- related policies. This thesis is in turn predicated on the idea that economic growth is typologically and historically sensitive. In other words, the transition to modern growth is an historical event charac- RELEVANCE OF FINDINGS FOR POLICY 311 terized by meaningful subphases. Furthermore, because of inherited economic, geographic, and institutional characteristics, different LDCS will undergo this transformation by following different patterns or subphases. Thus the policy focus elaborated here would not necessarily be relevant for types of countries very different from Taiwan- for example, countries large in size, rich in oil, or having a surplus of land. Mioreover any suggestions relevant to policy must be sensitive to the particular subphase that a country has reached in the transition to modern growth. In this volume we have concentrated on Taiwan as a successful example. The transferability of policy suggestions to other countries must be strictly based on the understanding that good FID policy, along with growth policy, must be sensitive to typological and historical considerations. Much can be said about what is unique or not unique in any particular experience and the consequent applicability or inapplica- bility to other countries. As was pointed out at the outset, no country's experience can ever be fully transferred. Taiwan unquestion- ably had some unique advantages: its initial endowment of human resources, its cultural heritage, its early colonial experience, its strong support by the United States. But some popular notions about the large quantitative role played by U.S. foreign aid early, and private investment later, are factually incorrect.1 Moreover Taiwan also had some substantial disadvantages not shared by many other contemporary LDCS: its initially unfavorable man-land ratio, its heavy population pressure over time, its felt need to spend a large part of its resources on national defense, its growing international diplomatic isolation. We recognize, when all is said and done, that readers will have to determine for themselves what is unique in, or transferable from, the Taiwan experience. We believe that many elements from the analysis in this volume, and the policy conclusions derived therefrom, have relevance in other contexts. As was pointed out earlier, the postwar transition to modern growth in Taiwan moved from the initial subphase of primary import substitution into that of export substitution in the early 1960s. By means mainly of a labor-intensive export drive, a landmark of transition growth appeared in about 1968, when the economy's

1. Although aid may have been of strategic importance in encouraging the important policy changesof 1961,public and private foreign capital contributed less than 6 percent of cumulative investment during the 1953-72 period. 312 RELEVANCE OF FINDINGS FOR POLICY

labor-surplus condition ended and real wages began to increase at an accelerated rate. Thus any respectable analysis of the essential growth phenomenon in such a labor-surplus, dualistic economy must explore the reallocation of labor from the agricultural sector to the nonagricultural sector and the changing pattern of the functional distribution of income. That changing pattern, measured by the relative size of the wage and property income shares, is brought about by changes in wage rates, factor endowment, and technology. The impact of growth on FID can be examined from three view- points: that of all families, that of urban families (receiving wage and property income), and that of rural families (receiving agricultural income as well as wage and property income). We naturally are interested in the relations between growth and equity for the entire population. We nevertheless found it useful, for both analytical and policy reasons, to focus first on the underlying sectoral level.

The Inequality of Family Income

The first specific empirical findings emanating from our analysis were these:

. For all households and urban households, virtual constancy in FID before 1968-the turning point marking off labor surplus from labor scarcity-gave way to significant improvement thereafter. • For rural households, significant improvement before 1968 gave way to virtual constancy thereafter.

These empirical findings support our basic thesis that FID equity indeed is a growth-sensitive phenomenon, as can be seen from the fact that, for urban and rural sectors separately and for the economy as a whole, this turning point demarcates markedly different phases of both growth and FID performance. Furthermore the transition involves the transformation of an agrarian economy into an industrial economy. Our findings indicate that the favorable impact of growth on FID in that context must occur in the relatively more dominant sector of the economy-that is, in agriculture before 1968 and in nonagriculture thereafter-if growth is to have a consistently favorable effect on FID over time. The unusually high priority Taiwan attached to the agricultural sector-to land reform, THE INEQUALITY OF FAMILY INCOME 313 infrastructural investments, and relative prices before commercialization-represents an example of the selection of the correct policy focus from the points of view of both growth and distribution in this general historical perspective. Analysis of the underlying causes of this aggregate performance can be conducted by identifying a reallocation effect which captures changes in the relative size of the agricultural and nonagricultural sectors, a functional distribution effect which captures changes in the relative shares of wage and property income, and a factor Gini effect which captures changes in inequality of distribution of a particular component of family income. What policy implications can be derived from this tripartite division of the causes of inequality? The main implication is that different types of policy are required to deal with the first two effects, which can be more directly related to analysis in the context of growth theory, than with the third. Thus it becomes important to know something about the relative quantitative significanceof the three effects as causes of overall FID equity. The empirical findings, more specific than those related to the degree of income inequality, once again support the general thesis that the nature of economic growth determines much of FID in both sectors of the dualistic economy. . For urban households the functional distribution effect, wvhich was highly unfavorable before 1968 and favorable after 1968, was a dominant cause of FID performIance. * For rural households the reallocation effect, which was favorable both before and after 1968, was a dominant cause of FID performance. The phenomena related to growth here are not only relevantbut dominant as explanatory causes of changes in the family distribution of income. As summarized in the foregoing findings, the difference between urban households and rural households is an important growth-relevant phenomenon. For the urban sector the accumulation of capital and human assets is at the heart of the industrialization effort. For this reason the functional distribution effect is a dominant cause of FID. For the rural sector, in contrast, the reallocation of labor from agricultural to nonagricultural production represents a much more crucial development issue. Consequently the reallocation effect turns out to be a dominant cause of FID performance. The implications of these findings help in the identification of the proper policy focus. For the urban sector the wage rate, 314 RELEVANCE OF FINDINGS FOR POLICY factor endowment, and technology choice-all elements affecting the functional distribution of income-are the dominant policy issues related to FID. For the rural sector the growth of rural-based industries and services alongside a productive agricultural sector, and the additional employment opportunities thus offered to rural households, are the dominant policy issues. To see more precisely how these growth-relevant forces affect FID, we first concentrated on rural families, which receive both agricultural and nonagricultural income. * For rural families agricultural income consistently was less equally distributed than nonagricultural income-that is, Ga > GO. . Over time, agricultural income became more equally distributed-that is, Ga declined. . Rural families received a surprisingly large and increasing share of income from rural industries and services, which were increasingly labor-using-that is, ka declined and O/O increased. As an economy modernizes, analysis of the equality of income distribution for rural families involves issues quite different from those affecting urban families. The main reason is the importance of agricultural production. Two central issues here are the equality of the distribution of agricultural income, which is the dominant income component for traditional rural societies, and the increase in the equality of the distribution of nonagricultural income associated with the growth of rural industries during the transition to modern growth. The foregoing empirical findings for rural areas show that the distribution of income from the traditional agricultural base is more unequal than that of the new income associated with rural-based industrialization. Worldwide concern about inequality in the distribution of agricultural income in rural communities has led to the laudable advocacy of direct government interference with the market mechanism where productive assets in agriculture (mainly land) are highly unequally distributed. In Taiwan early land reform, followed by increases in multiple cropping and the cultivation of new crops by the poorer (smaller) farmers, caused agricultural income to become significantly more equally distributed over time. That experience seems to indicate that land reform is an important input. But if the distribution of agricultural income is to be improved when THE INEQUALITY OF FAMILY INCOME 315 agricultural growth is rapid, a fairly equal distribution of landed assets is also required, and the "right" growth-oriented policies must follow such reform. How did the favorable reallocation effect cited earlier work to bring about a more equitable distribution of income for rural families over time? Because nonagricultural income was more equally distributed than agricultural income, the growth of rural industries and services made a substantial contribution to FID equity. Furthermore, when compared with urban industries, rural industries were found to be much more "labor using" (increasingly so over time). Thus the steady increase of opportunities in rural by-employment available to members of rural families, especially the poorer ones, greatly contributed to the complementarity of growth and FID. All these factors lie behind the reallocation effect's being a dominant factor contributing favorably to FID equity. The basic policy implication of the foregoing empirical findings for rural households is relevant to industrial location. As was pointed out in chapter three, nonagricultural income has always been an important component of rural family income in Taiwan. Given the spatially dispersed pattern of industrial location, the growth of rural-based industries and services offered new opportunities for employment and investment. These opportunities made it possible in later years for nonagricultural income to overwhelm agricultural income and become the most important source of rural family income. All the advantages of such a decentralized pattern of industrial location-for example, those related to agricultural modernization arising from direct contact with industrial activity to avoiding the costs associated with labor dislocation and transport, and to reducing urban congestion and social overhead expenditure-need not be elaborated here. But the development of rural industries and the abandonment of the all-too-frequent incenitives for urban concentration and agglomeration must be emphasized as prime policy recommendations emerging from our work. It is interesting to note, moreover, that most of the workers migrating from agriculture to nonagriculture were part-time or commuting farmers who were readily available for agricultural tasks at peak harvest time. Advocacy of a spatially dispersed pattern of industrial location provides a good example of the typological sensitivity required in policymaking. The pattern that emerged in Taiwan was largely the result of such demographic and geographic features as high population density, such topological features as the location 316 RELEVANCE OF FINDINGS FOR POLICY of principal ports and mountain ranges, and such historical features as the transport and energy networks established during the Japanese period. That pattern was also the result of government policies to equalize the cost of industrial energy and fuel throughout the island and to provide additional rural infrastructure as needed -policies which did not succumb to the normal subsidization and artificial encouragement of industrial agglomeration in urban areas. Consequently, competitive market forces yielded a dispersed pattern of industrial location and a labor-intensive output mix. Rela- tive to these forces, economies of scale played a minor role. When these basic demographic and geographic conditions are not met-as, for example, in the Philippines-and when, moreover, governments pursue policies intended to give special encouragement to large- scale, capital-intensive industry-as, for example, in Thailand and the Philippines-a centralized pattern of urban industrialization results. FID equity can be improved only in the context of a growth policy that is typologically sensitive. How did the functional distribution effect work to affect FID equity among urban households? First, the operation of the observed funtional distribution effect further supports the thesis that equity is a growth-sensitive phenomenon. As the conditions of labor surplus gave way to those of labor scarcity after 1968, the impact of the functional distribution effect on FID changed from being unfavorable to favorable. The reason is this. Only when labor becomes a scarce commodity, as evidenced by the sharp increase in the real wage, does the functional distribution effect become favorable. Two empirical findings explain more precisely the essential behavior of the functional distribution effect on urban FID. For urban households property income was more unequally distributed than wage income. The share of wage income declined relative to the share of property income before 1968 and gained at the expense of property income after 1968. Because property income was more unequally distributed than wage income, the functional distribution effect was unfavorable or favorable depending upon whether the labor share was falling-as it was before 1968-or rising-as it was after 1968. Before 1968 the real wage was relatively stable because of the continued surplus of labor. The urban family's share of wage income declined slightly, mainly because employment opportunities were not expanding at a pace THE INEQUALITY OF FAMILY WAGE INCOME 317 significantly greater than the rate of capital accumulation. That was in turn caused by the relatively weak labor-using bias of technology in urban industries. When the surplus of labor was exhausted after 1968, the increase in the real wage and the rapid increase of capital per worker (capital deepening) led to the expected increase in the wage share relative to the property share. In this way the functional distribution effect became favorable to FID after the turning point for conventional reasons. For the entire 1964-72 period, and disregarding additive factor components as in chapter five, it appears that overall income inequality declined mainly because of a reduction in inequality in the urban sector over time. This occurred despite the existence of a widening income gap between the urban and rural sectors. The declining trend in income inequality can be attributed to the rapid rate of labor absorption in light manufacturing industries, which were competitive in international trade before the turning point, and to the more conventional rise in wages thereafter. It often is said that growth in the 1960s and 1970s has failed to produce a more equitable distribution of family income. This statement has led, directly or indirectly, to the conclusion that radical government intervention is required to transfer assets from rich to poor, or at least to effect redistribution after the fact. The findings here, based on the analysis of the relations between growth and FID in Taiwan, indicate that the frequent conclusion in favor of continuous direct government intervention is not necessarily warranted. A relatively favorable initial distribution of assets clearly helped in Taiwan. But the major accomplishment of substantially eliminating the conflict between growth and FiD before the turning point was the result of three basic policies: the early attention to agriculture; the mild version of import substitution followed by thorough-going export-oriented industrialization; and the decentralization of industrial operations.

The Inequality of Family Wage Income

For the more disaggregate analysis of the inequality of family wage income, our conceptual framework recognized the formation of a heterogeneous labor force as crucial in industrialization. Differ- ences in education, age, sex, and family income characterize that heterogeneity. Distinctions were drawn among three types of issues 318 RELEVANCE OF FINDINGS FOR POLICY and reflected at three levels of analysis. At the first level we attempted to trace the differentiated structure of wage rates to principal characteristics of the labor force. At the second level we attempted to trace the inequality of individual wage income to the differentiated wage rate structure and the composition of the labor force. At the third level we attempted to trace the inequality of family wage income to the membership composition of families. The policy implications of the findings will be summarized separately for each of the three levels. At the first level, the analysis of the differentiated wage structure, we accepted the convention that differences in wage rates arising from differences in education and age are justifiable or warranted, but those arising from differences in sex and family influence are not. We acknowledge that not everyone will necessarily agree with this convention. The analysis at the first level nevertheless confirms that: Overall differences in wage rates reflected a mixture of both warranted and unwarranted causes. The policy implications of warranted causes clearly are neutral. Wage rates are supposed to differ for warranted reasons, and nothing should be done to influence them. The policy implications of unwarranted causes are stylized. Institutional discrimination against females and members of poorer families exists and should be removed. More significant, of course, is the issue of how stylized policy conclusions are to be related to growth. Using rural, town, and city residence as proxies for the increasing degree of industrialization, it was found that the modern commercialized milieu of large cities tends to evaluate sex and family influences with more sensitivity than the more tradition-bound milieu of rural communities. Institutional discrimination thus appears to be a by-product, perhaps an inevitable by-product, of modernization in its early phases. But because policy measures clearly affect more than the economic sphere, caution is required when dealing with wage differences that can be traced to institutional discrimination. For the education characteristic, it was found that there was no significant difference between large cities and rural communities in evaluating this warranted cause of differences in wage rates. In other words, the premium for education was about the same everywhere. Thus, in the more tradition-bound rural communities, market forces can more or less sensitively value this most important THE INEQUALITY OF FA-MILY WAGE INCOME 319 labor attribute. The policy implication again is negative or inactive. Government does not need, for example, to make a special effort in rural communities to render the labor market more perfect or to offer special inducement for labor migration to ensure a more efficient spatial pattern of educated manpower use. At the second level, the analysis of wage income inequality, the crucial issue about the relative overall importance of warranted and unwarranted causes can be addressed. . Discrimination by sex or family influence is not as quantitatively important as discrimination by education or experience (age). Together sex and family influence accounted for only 33 percent of the explained inequality. This type of conclusion provides an indication of what a policy that is calculated to eliminate institutional discrimination might accomplish, presumably at some cost. The findings at the first level of analysis show for differences in wage rates that labor markets in large cities tend to discriminate more against females and members of poor families than those in rural communities. But the composition of the labor force in the large cities apparently tends to compensate for this inequality. The findings at the second level of analysis indicate that institutional discrimination accounted for a smaller percentage of wage income inequality in large cities than in rural communities. In other words, females and members of poor families tend to get a larger share of better jobs in large cities. The implication of this finding for policy is that industrialization can be relied upon, despite the higher degree of institutional discrimination of wage rates, to bring about greater equality in the distribution of wage income. This conclusion tends to confirm the earlier assertion that policies to eliminate institutional discrimination should proceed cautiously. With an eye to future research, it can be added here that the analysis at the first level, which constitutes the focal point of what can be called traditional analysis, might give a misleading picture by concentrating only on institutional discrimination of wage rates. To assess the quantitative significance of institutional discrimination for wage income inequality, the changing composition of the labor force must also be known. The empirical findings presented here are a perfect illustration of this crucial point. At the third level, the analysis of family wage-income inequality, it was recognized that labor is a very heterogeneous factor of pro- 320 RELEVANCE OF FINDINGS FOR POLICY duction. Even the crude classification by sex, age, and education used in this analysis leads to thirty-seven grades of labor. Within our framework of reasoning, the unequal family ownership pattern- that is, the unequal composition of family membership by these grades-lies behind family wage-income inequality. Some "inferior" grades, such as the poorly educated old female, can be interpreted as being part of the marginal labor force; some "superior" grades, as part of the prime labor force. - The pattern of unequal ownership of the marginal labor force is a minor problem as far as overall family wage-income inequality is concerned. The policy implication is that government relief and welfare measures may help the marginal labor force, but have little impact on the basic problem of family wage-income inequality. Such a conclusion may at least force policymakers to think a little harder about the likely impact of policy options that seemingly are politically attractive. A related conclusion may do the same: * The most important cause of overall family wage-income inequality is the pattern of unequal ownership of high-grade workers. High grade, it will be recalled, can mean one or a combination of three attributes: prime age, male, and highly educated. If inequality is traced, for example, to differences in age and sex ownership- that is, to the contrast between families having a preponderance of prime-age males and families having a preponderance of old or very young females-there is no obvious government policy relevant to correcting this inequality. Any such policy would have to be very far-fetched, interfering with rules of family formation by preventing divorce or the formation of secondary nuclear families.2 The inequality of family ownership of the educated labor force is a different matter. The thesis of a tendency for the unequal distribution of the opportunity for higher education to perpetuate the inequality of family income has many adherents. According to this

2. The low causal effect attributable to age, by itself, gives us some confidence that the problem of life-time earning relative to observed earning may not be as serious as is sometimes believed. It was not possible, however, to examine this potentially important issue more rigorously in this volume. THE INEQUALITY OF TAXATION AND EXPENDITURE 321

thesis the wealthier families can provide better education, and better paying jobs, to their members-advantages that conceivably could be principal causes of family wage-income inequality. The findings here cast some doubt on this thesis, because as far as education is concerned the family turns out to be insignificant as the unit of labor ownership. This means that the degree of inequality of wage income of, say, 1,000 workers would remain the same, irrespective of whether the family affiliations of these workers are taken into consideration. For Taiwan this finding is not particularly surprising. The imperial examination system, institutionalized long ago in traditional China, continues to hold sway. Rigorous and impartial entrance examinations are annually held at all levels of formal education. Because wealthy families do not have the marked special advantages frequently encountered elsewhere, access to educational opportunities is thus relatively equal for all. Whether such a policy is feasible for other countries not having a similar cultural bias would seem to be at the heart of policy discourse in this general area.

The Inequality of Taxation and Expenditure

The analysis in this volume suggests a number of more specific policy conclusions based on findings related to patterns of taxation, disposable income, and family consumption. Economists and noneconomists have traditionally thought of taxes as an easy after- the-fact method of improving FID if the primary or growth-related outcome proves unsatisfactory. In this context, there usually is a secondary strategy concerned with minimizing the so-called disincentive effects of a taxation system that is too progressive. In Taiwan the system of taxation was found to be reasonable from the viewpoint of incentives-that is, it was not unduly progressive or regressive. In fact: * The distribution of the total tax burden was neutral with respect to its impact on the equity of distribution of family income. In other words, the degree of inequality of family income before and after taxes was about the same. The policy implication of this empirical finding lends further support to the overall conclusion of this volume: adequate FID performance is mainly the result of an 322 RELEVANCE OF FINDINGS FOR POLICY appropriate primary-that is, growth-related-strategy. Other work relating to fiscal impact seems to support this position.' Thus, even when the fiscal capacity of an LDC is relatively strong, as it is in Taiwan, direct government intervention after the fact will probably 4 do little to affect FID performance. A second and related finding also has an obvious implication for policy: * The total tax burden was neutral because the quantitatively more important and regressive indirect tax payments canceled the quantitatively less important and more progressive direct tax payments. Thus if the tax system is to be an instrument for bringing about a more equitable distribution of income, the tax basis should be shifted to direct taxation from its present overwhelming reliance on indirect taxation. This conclusion nevertheless is weakened because considerations other than equity considerations often prevail. During most of the period after 1962, Taiwan has been in a growth subphase of primary export substitution. The dominant phenomenon in this subphase is the export of labor-intensive goods, such as textiles, in exchange for the import of mainly producer goods, such as raw materials and capital goods. With the exhaustion of surplus labor around 1968 and the rapid increase in real wages subsequently, there has been a growing consensus that Taiwan now faces the transition into a sequence of secondary import and export substitution. That sequence aims first at the production, and later at the export, of those capital-intensive and skill-intensive producer goods which now are largely being imported. Given this change, it follows that Taiwan in the near future cannot hope to continue relying on cheap labor as the basis of its comparative advantage in foreign trade. The accumulation of skills, technology, and capital is likely to replace cheap labor and make unprecedented demands on Taiwan's private entrepreneurial resources. Consequently the primary emphasis in any future revisions of tax policy is likely to be on investment incentives, not on equity. For this reason, a shift

3. See for example Jacob Meerman, "Fiscal Incidence in Empirical Studies of Income Distribution in Poor Countries," AID Discussion Paper, no. 25 (Washington, D.C.: U.S. Agency for International Development, June 1972). 4. The possible redistributive effect of changes in the pattern of government expenditure, especially for such social services as health and education, is not dealt with here. FUTURE RESEARCH 323 from the regressive system of indirect taxation to a more progressive system of direct taxation may be inappropriate for Taiwan. Instead, movement toward a more progressive consumption tax, which would be very heavy on items likely to be consumed by high-income families, may be more appropriate. Entrepreneurs could still be encouraged to earn income and required to pay little tax as long as they reinvest their profits. Another interesting finding relates to expenditure: * For high- and low-income families the distribution of family expenditure on housing is significantly more unequal than that on other consumption. This finding indicates that a progressive consumption tax on housing, such as that based on the space or construction cost of residential units, could be considered as a major component of any proposed tax reform. Unlike the luxury consumption associated with night clubs, golf courses, and imported cars, housing is a popular item of mass consumption. It accounts for a larger portion of household expenditure than either savings or expenditure on education. Hous- ing, more than clothing and food, seems to symbolize class distinctions in the cultural milieu of contemporary Taiwan. If the experience in other countries is a guide, such class-differentiated consumption patterns will probably become socially and politically offensive in Taiwan as well. Consequently the introduction of progressive consumption taxation conforms well to the relatively egali- tarian pattern of income and the goals set for the future.

Future Research

We believe that the work of this volume, including the effort to derive general and specific policy conclusions from it, has demonstrated the desirability of integrating income distribution with the general framework of development theory. It also has demonstrated the complexity attached to many dimensions of the problem-dimensions that still are inadequately understood. We have not, moreover, even attempted to tackle some other issues, even though we recognize them to be important subjects for future analysis. Further investigation of the causation underlying the inequality of property income is one example. By making a highly selective and inductive effort, we have tried to contribute to a less ad hoc and more analytical treatment of the 324 RELEVANCE OF FINDINGS FOR POLICY distribution of family income as a dimension of development. By pointing out that at least one developing economy could "have its cake and eat it, too," we hope at least to make the tradeoff pessimists sit up and take notice. We have examined the whys and where- fores of that experience from a number of directions. We have concluded that the way transition growth is generated largely determines the levels of transition equity. By so doing we have perhaps contributed to the integrated deterministic theory of income distribution-a theory which still eludes us-and shed some light on the direction of policy choices that must be made in the meantime. What, then, are the implications for future research? Good policies for income distribution must be based on good theory. The prime focus of theoretical research must therefore be to attempt to explain empirically observed realities in order to understand the causal nexus between growth and equity. At this stage of understanding, much of that effort still is inductive. -Much attention still is paid to gathering, organizing, and processing data in accord with certain pretheoretical frameworks. The additive factor-components model and its combination with the linear regression technique illustrate the nature of these frameworks. Motivated by theoretical notions, they require a mathematical design that is broad enough for application to different types of problems. With more refined analytical tools, we can hope to separate the quantitatively important causes of inequality, such as access to educational opportunities, from the less important causes, such as sex discrimination. The policy focus could then be aimed at the important causes, and additional efforts could be directed at a determination of the feasibility and practicality of various policy options. Moreover it may be necessary to depart from subject areas familiar to the economist to those more tangential to traditional analysis. In this volume we hope merely to have demonstrated that it is feasible to make progress along these lines. PART TWO

The Methodologyof Gini Coefficient Analysis

THE SECOND PART OF THIS VOLUME is devoted to a systematic discussion of decomposition procedures and the derivation of decomposition formulas that use the Giri coefficient [G,] to measure the degree of inequality of a pattern of income distribution [Y = (Y,, Y2, ... Y.) ].' All decomposition equations used in part one amount to special cases developed irn this part. All the formulas deduced can be applied to empirical analyses of the inequality of income distribution, as will be emphasized through the use of numerical examples that show the computation procedures involved. This part has five

1. Many authors have worked out and published Gini decomposition formulas. They include, but perhaps are not limited to, the following. N. Bhatta- charya and B. Mahalanobis, "Regional Disparities in Household Consumption in India," Journal of the American Statistical Association, vol. 62, no. 317 (March 1967), pp. 143-61. V. M. Rao, "Two Decompositions of Concentration Ratio," Journal of the Royal Statistical Society, series A, vol. 132, pt. 3 (1969), pp. 418- 25. Mahar Mangahas, "Income Inequality in the Philippines: A Decomposition Analysis," World Employment Programme, Population and Employment Working Papers, no. 12 (Geneva: International Labour Organisation, 1975). Graham Pyatt, "On the Interpretation and Disaggregation of Gini Coefficients," Economic Jour- nal, vol. 86 (June 1976), pp. 243-55. Two other authors have published alternative indexes of inequality: Henri Theil, Economics and Information Theory (Amster- dam: North-Holland, 1967); Anthony B. Atkinson, "On the Measurement of Inequality," Journal of Economic Theory, vol. 2 (1970), pp. 244-63. The relatedness of their contributions to the work of this volume will be indicated where appropriate.

325 326 THE METHODOLOGY OF GINI COEFFICIENT ANALYSIS

chapters: . Basic Concepts * Testing Hypotheses * The General and Special Models of Additive Factor Components * Applications and Extensions of the Models of Decomposition * Regression Analysis, Homogeneous Groups, and Aggregation Error Chapter eight presents an investigation of the alternative definitions of the Gini coefficient, as well as of the pseudo Gini coefficient, when Y is given. In chapter nine we formulate a problem of testing hypotheses when an observable quality characteristic-such as education with high, medium, and low values-is associated with variations in the income levels in Y. The ideas developed in these two chapters are essential for the analysis in chapters ten, eleven, and twelve. Chapter ten is concerned with the derivation of decomposition formulas when Y has a finite number of additive factor components given by WI = (Wi, W4, ... , Wi), where i = 1, 2,..., p. Its purpose is to trace G, to G(Wi), the factor Gini coefficients defined for Wi. In addition to a general model, decomposition formulas are deduced for a linear model and a monotonic model, which are special cases of the general model when additional restrictions are postulated for Wi. Methods of approximation are developed when these restrictions are only approximately fulfilled, as often is the case in empirical work. Two other special cases are developed in chapter eleven. In one special case the sum of all values of W, in one component Wi is assumed to be zero, leading to a model of "income components with observation error." In the other special case several factor components are assumed to be negative. In chapter twelve a linear regression equation, estimated by the method of least squares, is combined with the model of additive factor components. Also in that chapter the analysis is directed at a situation in which Y is segmented into a finite number of subvectors:

y = (Y, Y,,y yq), yi = (yi yi, y ), ( = 1 2 q)

- 1 n2**i n t 2 n* 2 where Yi is interpreted as a homogeneous group. The purpose of this analysis is to trace G, to G(PY), the intragroup inequality, as well as to other effects. Finally the question of grouping error is addressed. THE METHODOLOGY OF GINI COEFFICIENT ANALYSIS 327

In empirical research on the problem of additive factor components, such as that in chapter three, the "grouped data" that often is used leads to a "grouping error" in the Gini coefficient. The problem is investigated as an application of the decomposition equation for homogeneous groups, and the possibility of future research on this issue is explored. CHAPTER 8

Basic Concepts

THE PURPOSE of this chapter is to define the basic concepts used in this volume and to illuminate them with numerical examples and figures. First, the Gini coefficient is defined in relation to the Lorenz curve, as is conventional. Second, two alternative definitions of the Gini coefficient are presented and proved: one in relation to weighted income fractions; the other to the average gap between income fractions. Third, the pseudo Gini coefficient is defined in relation to the pseudo Lorenz curve, which obtains when incomes are not necessarily ranked in a monotonically nondecreasing order. These concepts constitute the foundation for the discourse on methodology in subsequent chapters.

Definition of the Gini Coefficient

Suppose there are n families with income Yi (i = 1, 2, ... , n) and compute the income fractions yi:

(8.1a) Y = (Y1, Y2, ... , Y.) > 0,

(8.1b) s, = Y 1 + Y2 + . .. + Yn > 0, and

(8.1c) y = (Yi, Y2, . , Y.) = (Y1/sy, Y 2 /sy, ... , Y./sy), where (S.1d) YI + Y2 + ... + Y. = 1 and

(8.1e) Y < Y2 < ... _< Yn. In equation (8.1b) s,, is the sum of incomes for all families; in equation (8.1c) the income fractions [yi] form a system of weights.

828 DEFINITION OF THE GINI COEFFICIENT 829

Figure S. 1. The Lorenz Curve

I I 0/4

------t------L;7---

X /t~~orenz curve Y .

<<, 4_~~~~~~~~~~~~~Y -02=

source:Constructed bv the autliors.

Notice that family incomes are arranged in a monotonically nondecreasing order, such that the first family is poorest and the last family is wealthiest. The Lorenz curve is a real-valued function defined on (1/n, 2/n, ... , n/n): (8.2a) Ly (j/n) = Y + Y2 + . .+ Y. (j = 1, 2, n) For example, when n equals 4:

(8.2b) Y - (Yl, Y2,YS, Y4) = (0.1, 0.2, 0.3, 0.4). If B denotes the area under the Lorenz curve of the unit square of figure 8.1, the Gini coefficient is defined as: (8.3) G,, = (1/2 -B)/(1/2) = -2B. 330 BASIC CONCEPTS

In words, G, is the area above the Lorenz curve inside the triangle OED, expressed as a fraction of that triangle's area, which is 1/2. For the numerical example in equation (8.2b) the Gini coefficient is 0.25. The Gini coefficient, according to its definition in equation (8.3), is a nonnegative fraction. It takes on extreme values of 1 to represent extreme inequality and zero to represent extreme equality. For these extremes:

(8.4a) Y, = Y2 = ... = Yn, which implies that G, = 0, and Eperfect equality]

(8.4b) Y1 = Y2 = ... = Y-, = 0, which implies that G, = 1. Eperfect inequality] When equality is perfect, the Lorenz curve coincides with the diag- onal OD in figure 8.1. When inequality is perfect and n is large, the Lorenz curve coincides -with the unit square's edge OED. Because the Gini coefficient of Yi is defined in relation to income fractions [Y], the following result is elementary: if:

(8.5a) Z = (kY1, kY2, .. ,Y), then: (8.5b) G. = Gy. In words, if the incomes of all families change by a common multiple, the Gini coefficient will not change.

The Gini Coefficient as Related to the Rank Index of Y

The intuitive explanation of the geometrically defined Gini coefficient as a measure of income inequality can be seen from two alternative definitions, the first of which is presented in this section.

THEOREM 8.1. The Gini coefficient of Y, as defined in equation (8.3), is:

G, = au,b- , where (a) a = 2/n, THE GINI COEFFICIENT AS THE AVERAGE FRACTIONAL GAP 881

(b) a = (n + 1)/n, and

(d) Yl < Y2 < Y

(e) Xl = 1, X2 = 2, . . . , Xn = n.

In this theorem Xi is the income rank of the ith family. The term uU is the weighted average of income ranks and will be referred to as the rank index of Y. Theorem 8.1 states that the Gini coefficient is a linear transformation of the rank index of Y. Using the figures from the numerical example in equation (8.2) gives:

(8.6a) u, = 1(0.1) + 2(0.2) + 3(0.3) + 4(0.4) = 3 and

(8.6b) Gv = (2/4) (3) - 5/4 = 0.25.

To prove theorem 8.1 observe that the area above the Lorenz curve is:

1- B = (1/n) (yi/2 + Y2 + *.. + Yn) 2 + (l/n) (y2/ + y3 + ... + y.) + . + (l/n) (yn)

= (1/n)u,- (1/n) (y1 + y2 + ... + )/2

by theorem 8.1 (c)

= (1/n) (u, - 1/2) by equation (8.ld).

Thus:

G = 1 - 2B by equation (8.3)

= 1 - 2[ - (1/n) (u,-1/2)]

= 2u,/n - (n + 1) /n.

This proves theorem 8.1 and provides the first alternative definition of the Gini coefficient.

The Gini Coefficient as the Average Fractional Gap

Consider the following numerical example of a pattern of monotonically ranked income fractions, as defined in equation (8.1c):

(8.7a) Y = (Yl, Y2,Y3, Y4, Y5) = (0.05, 0.10, 0.15, 0.30, 0.40), 332 BASIC CONCEPTS

(8.7b) 0 < Yi < Y2 < y3 < y4 < y5, and

(8.7c) 1 = Yl + Y2 + Y3 + Y4 + Y5.

Now define the following fractional gaps:

(8.8) y,- y Y2-Y1 Y3Y- Y4-Y1 - -Y5-

0 Y2Y2 Y3-Y2 Y4-Y2 Y5-Y2

0 0 Y3 - Y3 Y4 - Y3 Y5- Y3

0 0 0 Y4 - Y4 Y5 - Y4

0 0 0 0 Y5-Y5_ Fo 0.05 0.10 0.25 0.85

0 0 0.05 0.20 0.30

0 0 0 0.15 0.25

O O 0 0 0.10

-00 0 0 0

Because the values of yi are monotonically ranked according to expression (8.7b), the elements of this matrix indicate all the nonnegative income gaps between all possible pairs of families. Denote the sum of all these numbers by S>, which in the general case of n families is defined as:

(8.9a) S = E (yi - yi) for all i > j.

Using the figures from the numerical example in equation (8.8) gives:

(8.9b) S, = 0.05 + 0.10 + 0.25 + 0.35 + 0.05 + 0.20 + 0.30 + 0.15 + 0.25 + 0.10

= 1.8.

A term such as Y4 - Y2 = 0.20 indicates the gap of income fractions between a wealthy family (the fourth) and a poor family (the THE GINI COEFFICIENT AS THE AVERAGE FRACTIONAL GAP 333 second) and measures the extent or degree of inequality between them. In equation (8.9a) the sum of all fractional gaps is S,. The average fractional gap for n families is Sn/n. When equality is perfect, as in equation (8.4a), the average fractional gap [S,/n] obviously is equal to zero. The following theorem states that the Gini coefficientis precisely the average fractional gap':

THEOREM 8.2. G, = Sn/n, where S, is defined as in equation (8.9a). Proof: Take the sum of positive and negative entries of the matrix on the left-hand side of equation (8.8) separately, which gives:

U-uv= [ny1 + (n -l)Y 2 + . .. + lyn] by theorem 8.1(c)

=u - [nyl + nY2 + ... + nyn]

+ EOYI + lY2+ 2y3 + . . . + (n-l )y.]

=u -n + [OY + ly 2 + 2y3 + . + (n- )Yn by equation (8.1d)

=U -n- + (Yl + Y2 + + yn)

+ [Oy1+ ly2 + 2y + ... + (n- 1)y] = - n- 1 + u, by theorem8.1(c)

2u1, - (n + 1)

= n[ (2/n)u - (n + 1)/n] = nG1, by theorem8.1. This completesthe proof. The numerical example in equation (8.7) can verify theorems 8.1 and 8.2, whichposit that the Gini coefficientcan be calculated as the averagefractional gap: G, = Sn/n = 1.8/5 = 0.36,

1. Bhattacharya and Mahalanobis, in their analysis of regional disparity in household consumption, give the equivalence of the two definitions of the Gini coefficient. If, in their model, every region contains exactly one household, their special case becomes equivalent to the theorem stated here. N. Bhattacharya and B. Mahalanobis, "Regional Disparities in Household Consumption in India," Journal of the American Statistical Association, vol. 62, no. 317 (March 1967), p. 149. 334 BASIC CONCEPTS or as a linear function of the rank index of Y: u, = 1(0.05) + 2(0.10) + 3(0.15) + 4(0.30) + 5(0.40) = 3.9; G, = (2/5) (3.9) - 6/5 = 0.36.

The Pseudo Gini Coefficient

Let Y = (Y1, Y2, .. . , Y.) be an ine.)me distribution pattern which is not necessarily monotonically arranged-that is, which may not satisfy the conditions of expression (8.1e). Now define a pseudo Lorenz curve as: (8.10) Lt(j/n) = Y1 + y2 + ... + yj. (j = 1, 2, ... ,n) For the following numerical example:

(8.11) y = (y', Y2, y3, y4) = (0.2, 0.4, 0.1, 0.3), the pseudo Lorenz curve is indicated by the curve A'B'C'D' in figure 8.2. When B denotes the area under the pseudo Lorenz curve, a pseudo Gini coefficient can be defined in a way similar to equation (8.3): (8.12) = 1 2B. Notice that the only difference between the Gini coefficient defined in equation (8.3) and the pseudo Gini coefficient defined here is this: for G, the terms of the expression Y = (Y1, Y2, . .. , Y.) are arranged in a monotonically nondecreasing order, thus satisfying the conditions of expression (8.1e); for G, they are not so arranged. Theorem 8.1 then rigorously implies:

THEOREM 8.3. The pseudo Gini coefficient of Y is:

G, = -a/-, where

ty = XIYI + X2Y2+ . . . + X,,Y., and where a, ,S, and Xi are defined as in theorem 8.1. The term a, in theorem 8.3 will be referred to as the pseudo u index. To illustrate, the numerical example in equation (8.11) can be used to calculate the pseudo Gini coefficient: (8.13a) u,, = 1(0.2) + 2(0.4) + 3(0.1) + 4(0.3) = 2.5;

(8.13b) Gy = (2/4) (2.5) - 5/4 = 0. THE PSEUDO GINI COEFFICIENT 335

Figure 8.2. The Pseudo Lorenz Curve

y DI

(Y4 0.3

P s e u d | UsB = 0.4 Pseudo Lorenz curve 0 0)

0 0 ~~~~~Y20.4 oLorenzcurve)

______. = 0.2

0 1/4 2/4 3/4 4/ E

Source: Constructedby the authors.

The pseudo Gini coefficient, as defined, is an abstract, geometrical concept which will be applied in subsequent chapters. When an income distribution pattern [Y = (Y1 , Y2, ... , ) is not necessarily monotonically arranged, there can be a permutation [(i1 , i2, . . . , in)] of the n integers such that:

(8.14a) y* = (Yj,, Yi2, .. . ,Yi) satisfies: (8.14b) Yi, > yi2 > ... >Yf In words, Y* is a rearrangement of Y into a monotonically nondecreasing order. For example: Y* = (0.1, 0.2, 0.3, 0.4) 836 BASIC CONCEPTS in the numerical example of equation (8.2b) is a rearrangement of: Y = (0.2, 0.4, 0.1, 0.3) in equation (8.11). The difference between the Gini coefficient of Y [G( Y*)] and the pseudo Gini coefficient [GJ can be defined as a Gini error [E]: (8.15) E = G(Y*) - Ž2, 0, which always is nonnegative. From the numerical examples in equations (8.2b) and (8.11) it can be seen that:

(8.16) E = G(Y*)- = 0.25 - 0 = 0.25 > 0. [see equations (8.6b) and (8.13b)] Equation (8.16) shows that the Gini coefficient is at least as large as the pseudo Gini coefficient. The Gini error [E] will later be proved to be nonnegative. A geometric interpretation of the Gini error is evident from:

(8.17) E (1 - 2B) - (1 - 2B) by equations (8.3) and (8.12)

2(B - B).

Thus the area between the pseudo Lorenz curve and the Lorenz curve is equal to one-half the value of the Gini error (see figure 8.2). In that figure the area corresponding to B - B is shaded. In figure 8.3 a pseudo Lorenz curve [A"B"C"D"] is shown for y = (0.4, 0.3, 0.2, 0.1) which is in a reverse monotonic order, that is, a monotonically nonincreasing order. This curve is now rotationally symmetrical with the Lorenz curve ABCD from figure 8.1 with respect to the 45-degree line OD". Thus the shaded area in figure 8.3 is:

B - B = 2A = 2(1/2 - B), where A is the area between the Lorenz curve and the line OD", and the Gini error becomes:

(8.18a) E = 2(B - B) = 2(1 - 2B) = 2G(Y*) by equation (8.3), which implies that: (8.18b) G(Y) = -G(Y*) by equation (8.16). THE PSEUDO GINI COEFFICIENT 387

Figure 8.3. The Pseudo Lorenz Curve for an Inverse Wage Pattern

g ~~~~~~~~~~~~~~~Dt

Pseudo Lorenz curve for inverse wage pattern

0 1/4 2/ 4 3/ 4 4/4 E

Source: CSonstructed by the authors.

For later reference, this equation can be summarized as: THXEOREM8.4. For a monotonically nonincreasing pattern of income distribution: 0(Y) = that is, the pseuzdoGini coeffi:cunt is the negative of the Gini coefficient. CHAPTER 9

Testing Hypotheses

CERTAIN QUALITY CHARACTERISTICS, denoted by C, can be intuitively identified as relevant to the analysis of causes of income inequality:

(9.1) c = (cl < C2 < ... < ordinally ranked values of a quality characteristic affecting G J For example, C can represent the sex characteristic and have values of cl for female and c2 for male; it can represent the education characteristic and have values of cl for low education, c2 for medium education, and c3 for high education; or it can represent the age characteristic and have values of ci, where i is the age of the head of household or income earner. Whenever C is given, the presumption -that is, the hypothesis-is that its values will affect the levels of family income. In such a situation the minimum information to be postulated is that the values [ci] are ordinally ranked attributes that contribute to the earning power of families. For the ranking in equation (9.1), cl is assumed to make the least contribution to the level of family income; cm the greatest contribution. If C is education, the values of the education characteristic are assumed to contribute to higher income levels in an ascending order:

(9.2) cl < c 2 < C3. Elow 1< [medium] < high 1 educationJ - [education -L [education] Assume that such a quality characteristic as education is given

38 TESTING HYPOTHESES 339

Table 9.1. Numerical Example of Income Fractions, Income Ranks, and Education Ranks for Five Families

Family Family Family Family Family Variable 1 2 5 4 5

Income fraction, y, = 0.05 y2 = 0.10 YS = 0.15 y4 = 0.30 y5 = 0.40

Income rank x, =1 X,=2 x, = 3 X4 = 44 x = 5 Education rank r, = 5 r2 = 4 r3 = 1 r4 = 2 r6 = 3

Value of education characteristich CB = H C3 = H cl =L cl = L C2 = M

Source: Constructed by the authors. a. These values are from the numerical example in equation (8.6a) in chapter eight. b. In accord with expression (9.2), cl and L stand for low education, c2 and M for medium education, and Cs and H for high education. and that every family receives a value [ci] for that characteristic [C]. The n families can then be ranked with respect to C (table 9.1). In this table the first family receives the lowest income rank because it is the poorest; curiously it also receives the highest education rank because its income earner has the most education. When the number of families [n] is large and the number of characteristic values [m] is small, the n families are classified in m education groups. Families belonging to the same group-that is, families with tied rank-are arbitrarily assigned a numerical ranking. In the numerical example, the first two families received the two highest education ranks: family one's education rank [r,] is 5; family two's [r2] is 4. The alternative way of assigning ranks to these two families is: r, = 4; r2 = 5. In general the following per- mutations of the first n integers can stand for the characteristic ranking of the n families:

(9.3) r = (ri, r2, . . . , and it can be hypothesized that a higher characteristic rank should lead to a higher income rankl:

HYPOTHESIS 9.1. The relation ri > rj implies that yi > yj or Xi > Xi.

1. Graham Pyatt of the World Bank has presented an ingenious interpretation of the Gini coefficient as the expected value of a game and demonstrated the usefulness of that interpretation to socioeconomic problems relevant to 340 TESTING HYPOTHESES

If the characteristic is education, the hypothesis is that higher education should lead to higher income. Because the first two families in table 9.1 are the most educated, and yet the poorest, they clearly violate this hypothesis. The purpose of this chapter is to investigate how a hypothesis, such as hypothesis 9.1, can be systematically tested.

Testing Hypotheses by Supporting and Contradicting Gaps

Postulate the income fractions [y3, income ranks [Xi], and characteristic ranks [ri] as follows:

(9.4a) y = (YI, Y2, e , Y.), where y, < y2 < ... < yf/ and [incomefractions] EYi = 1;

(9.4b) X = (Xi,X2, . .. ,X.) = (1, 2, .. n) [income ranks]

(9.4c) r = (ri, r 2 , . .. , rn), which is a permutation of (1, 2, . . ., n). [characteristic ranks] Notice that the pattern of income fractions [y] is arranged in a monotonically nondecreasing order in accord with the conditions of expression (8.1e). Consequently the pattern of income ranks [X] is just the natural order of the first n integers.The pattern of characteristic ranks [r] is a permutation of the first n integers, such that ri > rj implies that the ith family should have a higher income than the jth familyby null hypothesis9.1. When y is given as in equation (9.4a), the nonnegativeincome gaps [yi - yj] between all pairs of familiescan be definedas in equation (8.8). When Xiand ri are given in addition,these income incomeinequality, such as discriminationand migration.The approach adopted in this chapter is tantamount to an alternative interpretation of the decomposition of Gini coefficientsin relation to testing a null hypothesis about the role of quality characteristicsin the analysis of income distribution equality. This approach will be adhered to throughout this chapter. Graham Pyatt, "On the Interpretation and Disaggregationof Gini Coefficients,"Economic Journal, vol. 86 (June 1976), pp. 243-55. TESTING HYPOTHESES BY SUPPORTING AND CONTRADICTING GAPS 341 gaps can be classified into two types: a type that supports the hypothesis; a type that contradicts it. In the numerical example of table 9.1, the income gap between family one and family three clearly contradicts the hypothesis. On the other hand, the income gap between family four and family five clearly supports the hypothesis. Use that numerical example to see how the two types of gap can be systematically identified, and construct the following matrix from the characteristic ranks in equation (9.4c):

(9.5) r1 r2 rs r4 r5

ri 0 r 2 -r 1 r 3 -ri r4-rl r5-r 1

r2 0 r3 -r 2 r4-r 2 rT-r2

r3 0 r 4 -r 3 r 6 -r 3 =

r4 0 r- r4

r5 0

0 -1 -4 -8 -2

0 -3 -2 -1

0 1 2.

0 1

0- An element of this matrix indicates the difference, or gap, between the characteristic ranks of a pair of families. Because the income fractions [yi] are monotonically ranked in accord with equation (9.4b), a negative entry in this matrix indicates that the hypothesis is contradicted; a positive entry, that it is supported. In the right- hand matrix, all negative entries are in italics. They indicate all pairs of families which contradict the hypothesis. [In the matrix of equation (8.8) the corresponding family pairs are also in italics.] The other entries indicate the supporting gaps. Let S+ denote the sum of all supporting gaps and S- the sum of all contradicting gaps. Formally the definitions of S+ and S- thus 842 TESTING HYPOTHESES are: (9.6a) S, = S+ + S-, where

(9.6b) S- = E (yi - yi) Ž 0 for i > j and ri < r,, and [contradicting gaps] (9.6c) S+ = E (y -y,) > 0 for i > j and ri > r,. [supporting gaps] Equation (9.6a) shows that S&, which is defined in equation (8.9a) as the sum of all fractional gaps, is partitioned into two nonnegative components, S+ and S-. Figures from the numerical example of table 9.1 give: (9.7a) S, = 1.3 + 0.5 = 1.8, where (9.7b) S- = 0.05 + 0.10 + 0.25 + 0.35 + 0.05 + 0.20 + 0.30 = 1.3 and (9.7c) S+ = 0.15 + 0.25 + 0.10 = 0.5. In the example, S- is larger than S+, a relation which indeed subjects to doubt the hypothesis that education contributes to income- earning.

Gini Decomposition for Hypothesis Testing

Theorem 8.2 showed the Gini coefficient to be the average fractional gap [Sd/n]. This definition, or interpretation, is quite independent of any quality characteristic [C], as postulated in equation (9.1). When a quality characteristic [C] and a corresponding characteristic rank [r] are given, the result in equation (9.6) immediately shows that the Gini coefficient can be decomposed into an average supporting gap [s+] and an average contradicting gap [s-]: (9.8a) G, = s+ + s- by equation (9.6) and theorem 8.2, where (9.8b) s+ = S+/n > 0 and [average supporting gap] (9.8c) s- = S-/n > 0. [average contradicting gap] NET SUPPORTING GAP 343

The values in equation (9.7) give:

(9.9a) G, = S,/n = 0.36 = s+ + s- = 0.10 + 0.26 = 0.36, where

(9.9b) s+ = S+/n = 0.5/5 = 0.10 and [average supporting gap] (9.9c) s- = S-/n = 1.3/5 = 0.26. [average contradicting gap] G, can now be interpreted as the "total variation" of yi. Before a characteristic is introduced, all variations [y. - yj] are unexplained. After such a characteristic as education or age is introduced, a part of the variation, corresponding to s+, can be explained by that characteristic; the other part, corresponding to s-, cannot be explained by that characteristic. In fact, s- reduces the explanatory power of s+.

Net Supporting Gap

For testing the hypothesis, it is natural to find out the comparative magnitudes of s+ and s-. If s+ is much larger than s-that is, if the average supporting gap overwhelms the average contradicting gap-we would tend to accept such a null hypothesis as 9.1. Thus it is natural to define a net supporting gap as:

(9.10) N = + -s-, [net supporting gap] and to accept the null hypothesis when N is positive, reject it when N is negative, or regard it as irrelevant when N is close to zero. The purpose of this section is to show that N is precisely the pseudo Gini coefficient defined in theorem 8.3 of chapter eight. Recall that a pseudo Gini coefficient [G( Y)] can be defined for any pattern of income [Y = (Y1, Y2, ... , Y.)] which is not necessarily monotonically ranked. When y, X, and r of equation (9.4) are given, the following weighted ranks can be defined:

(9.lla) u, = ly, + 2y2 + ... + ny.; [weighted income rank] 844 TESTING HYPOTHESES

(9.llb) u,, = rly1 + r2y2 + ... + rnyn. [weightedcharacteristic rank] Respectively applying theorems 8.1 and 8.3 gives:

(9.12a) Gy = (2/n)u.1 - (n + 1)/n and [Gini coefficient]

(9.12b) 0, = (2/n)i - (n - 1)/n. [pseudo Gini coefficient] To illustrate with figures from the numerical example: (9.13a) u,, = 1(0.05) + 2(0.10) + 3(0.15) + 4(0.30) + 5(0.40) = 3.9; (9.13b) Q, = 5(0.05) + 4(0.10) + 1(0.15) + 2(0.30) + 3(0.40) = 2.6 = 1(0.15) + 2(0.30) + 3(0.40) + 4(0.10) + 5(0.05) = 2.6. Hence:

(9.14a) G. = (2/5) (3.9) - 6/5 = 0.36;

(9.14b) G. = (2/5) (2.6) - 6/5 = -0.16. Notice that the italicized expression in equation (9.13b) is merely a rearrangement of the terms of i4-the weighted characteristic rank of equation (9.llb)-into an ordering by the characteristic rank. Now the income fractions (yi) are not monotonically arranged. Thus O;,in equations (9.12b) and (9.14b) indeed is the pseudo Gini coefficientas defined in theorem 8.3 of chapter eight. By comparing equation (9.13) with equation (9.7b) it can be seen that the contradicting gap [S- = 1.3] is the difference between the weighted income rank [u, = 3.9] and the weighted characteristic rank [4 = 2.6]. This relation may be stated as: LEMMA9.1. S_ = U, - UY.

Proof: S- = E (yi - yi) for i > j and ri < r1 = dly- + d2Y2 + . . . + d( y.

= (Ul - V1) YI + (U2 - V2)Y2 + ... + ( U. - Vn.)Yn. NET SUPPORTING GAP 845

It can be seen that the coefficient di of yi is the difference between ui and vi, where ui is the number of families with an income rank lower than the ith family and a characteristic rank higher than the ith family, and where vi is the number of families with an income rank higher than the ith family and a characteristic rank lower than the ith family. It is obvious that:

ri = Xi + Vi -Ui, for in order to compute the characteristic rank [ri] of the ith family from its income rank [Xi], ui must be subtracted from Xi and v1 must be added to Xi. Thus:

di= -ui = i- ri. Hence:

SL=(Xi - ri)y, + (;X2 -r2)Y2 + ... + (X. - r.)y.

= UV - U,,. This completes the proof. Lemma 9.1 will now be used to prove the following theorem, which states that the net supporting gap [N = s+- s-] defined in equation (9.10) is precisely the pseudo Gini coefficient. THEOREM9.1. 0G = S+ - S . Proof: s- = S,,/n by equation (9.8c)

= l/n[u, - i,,] by lemma 9.1

[((2/n)u, - (n + 1 )/n) - ((2/n)iz. - (n + 1 )/n) ]/2

(G., - G,)/2 by equation (9.12)

(s+ + s -G,)/2- by equation (9.8a);

s+ + s --G = 2s-. Thus:

G, = s+ - -. This completes the proof. Theorem 9.1 states that the pseudo Gini coefficient is the difference between the average supporting gap and the average contradicting gap and thus is the net supporting gap. The hypothesis .346 TESTING HYPOTHESES is supported when G, is positive-that is, when the supporting gaps [S+] overwhelm the contradicting gaps [S-]. Similarly the hypothesis is rejected when G0 is negative. In summary: (9.15a) GQ = s+ + s-; (9.15b) Gz,= s+-s-; (9.15c) G,, = Q + 2s-, or E = G,-G =2s- >O. Thus the Gini coefficient [G,] is the sum of the average supporting and contradicting gaps; the pseudo Gini coefficient [G] is their difference. In addition, the difference between G, and G,, is 2s-, which always is nonnegative. This proves that the Gini error [E] is nonnegative, as was stated in equation (8.16).

Graphic Summary of the Gini and Pseudo Gini Coefficients

It has been shown that the Gini coefficient and the pseudo Gini coefficient can be defined when the income fractions [y], income ranks [X], and characteristic ranks [r] of equation (9.4) are given. The relation between G, and G0, is graphically summarized in this section. Let s+ be measured on the horizontal axis in figure 9.1 and s- on the vertical axis. Because the value of G, lies between zero and one, all possible combinations of the coordinates (s+, s-) can be represented by points in the equilateral triangle OAB (OA = OB = 1). The parallel and negatively sloped 45-degree lines represent iso Gini coefficient contour lines. Thus all points on the line FF", for example, have a Gini coefficient equal to OF. The line AB represents perfect inequality-that is, G, = 1. Also in figure 9.1 the 45-degree line OR3 divides the triangle OAB into two regions: r+ lies below OR3; r- lies above OR3. A point such as P in the region r+ indicates that the average supporting gap [s+] overwhelms the average contradicting gap [s-] and hence that empiricalevidence supports a hypothesissuch as 9.1. A point such as Q on or near OR3 indicatesthat empiricalevidence does not support the hypothesis.A point such as T in the region r- indicates that empiricalevidence contradicts the hypothesis. The straight lines parallel to OR3 are the equal pseudo Gini contour lines. On the line FF", the value of the pseudo Gini is OF.The GRAPHIC SUMMARY OF THE GINI AND PSEUDO GINI COEFFICIENTS 347

Figure 9.1. Iso Gini Coefficient Contour Lines (OA = OB 1)

s- 8 Rs~~~~~~~R B

Xs+t'~~~~~~~~F O F' A Source: Constructed by the authors. pseudo Gini coefficient is positive in r+ and negative in r?. Further- more it can be seen that: (9.16) -1 < (, < 1. A higher positive value of CT,is represented by a contour line closer to point A; a higher negative value, by a contour line closer to point B. A positive value of G, close to 1 would therefore indicate that the hypothesis is strongly supported; a negative value close to -1, that the hypothesis is strongly contradicted. Two extreme cases are to be mentioned: (9.17a) ri = Xi, which implies that s- = 0 and G, = (;u = s+; (9.17b) ri = n - (i + 1), which implies that s+ = 0 and

G, = -G, = sr. 348 TESTING HYPOTHESES

The economic interpretation of equation (9.17a) is that the correlation between the income rank [xi] and characteristic rank [ri] is perfect and positive. In this case the contradicting gap vanishes and the Gini coefficient equals the pseudo Gini coefficient [see equations (9.11) and (9.17)]. Points on the horizontal axis OA in figure 9.1 represent this special case. The economic interpretation of equation (9.17b) is that the correlation between the income rank [Ex] and characteristic rank [ri] is perfect and negative. The supporting gap vanishes, and the pseudo Gini coefficient equals the negative value of the Gini coefficient. Points on the vertical axis OB represent this special case (see theorem 8.4).

Correlation Characteristics

Now express the pseudo Gini coefficient as a fraction of the Gini coefficient:

(9.18a) R = GJGa = + + by equation (9.15);

s+ + s- 1 + s-/s+ In economic terms R is the net supporting gap expressed as a fraction of the "total gap"-that is, as a fraction of the sum of the average supporting and contradicting gaps. To arrive at another interpretation of R, the ordinary correlation coefficient r(x,y) between two vectors, x and y, is introduced to define:

(9.19a) r(y,X) = cov(y,X)/o-,or for y = (YI, Y2, . , yn) and

X= (1,2, ... n);

(9.19b) r(y,r) = cov(y,r)/ loa,, for r = (r1 , r2, . . . ),

(9.19c) Ur = ax- Therefore r(y,X) is the ordinary correlation coefficient between the family income fractions and the income rank [X]; r(y,r) is the ordinary correlation coefficient between those fractions and the characteristic rank [r]. Notice that equation (9.19c) is valid because both terms represent the standard deviation of the first n integers. In equations (9.19a) and (9.19b) the notation cov(x,y) CORRELATION CHARACTERISTICS 349 stands for the covariance between x and y. This leads to the following theorem: THEOREM9.2. R = r(y,r)/r(y,X). Proof: We know that: 1=/n by equation (8.1d); r= = (1 + 2 + ... + n)/n = n(n + 1)/2n = (n + 1)/2;

cov(y,r) = E (yi - y) (ri - f) = E yiri -nf

= u- nyr by equation (9.llb)

- n(n + 1)/2n

= - (n + 1) /2 = (n/2) [(2/n)t - (n + 1) /n] = (n/2) G, by equation (9.12b). Similarly:

cov(y,X) = (n/2)G 5. Thus: r(y,r)/r(y,X) , = (n/2)G/aoo]/[(n/2)G)/ow)j by equation (9.19)

= R by equation (9.18). This completes the proof. Therefore R can also be considered as a ratio of two ordinary correlation coefficients-that is, r(y,r) expressed as a fraction of r(y,X).2 From equation (9.18b) it can be seen that the value of R is completely determined by the ratio of s- to s+. In figure 9.1 the radial lines OR1, OR2, ... , OR6 then represent iso R contour lines. In the region r+, R is positive, and a radial line such as OR1 takes on a value close to 1. In the region r-, R is negative and a radial line such as OR6 takes on a value close to -1. It directly follows from expression (9.16) and equation (9.18)

2. There thus are two alternative interpretations of R as defined in equation (9.18) and theorem (9.2). Pyatt first suggestedthe second interpretation in a private discussionwith the authors. 350 TESTING HYPOTHESES that R lies between 1 and -1. Two types of case-a positive R and a negative R-can be identified: (9.20a) -l 0 if and only if 0 < G,, or s+ > s-; [positive R] (9.20c) R < 0 if and only if G0 < 0 or s+ < gs. [negativeR] In words, R is positive if and only if the pseudo Gini coefficient is positive. When R is positive, the average supporting gap [s+] overwhelms the average contradicting gap [s-]. The ratio of G, to G,, is R. Their sum is: (9.21a) G,,+ G =, G(1 + R) = 2s+ > 0, and their difference is:

(9.21b) G,- = G,(1 - R) = 2s- > 0. Thus their sum is twice the average supporting gap, or 2s+; their difference is twice the average contradicting gap, or 2s-. Both are nonnegative numbers. So far certain basic ideas have been developed for testing hypotheses when the pattern of income of n families is associated with one ordinal characteristic [C]. This method can be applied to other related empirical problems of hypothesis testing. But our purpose is to apply these ideas to the derivation of the various decomposition formulas used in the earlier chapters of this volume. CHAPTER 10

The General and Special Models of Additive Factor Components

As NOTED EARLIER, a situation is frequently encountered in which family income is the sum of several types of income. Consider the example used in chapter three with five families and three income components (table 10.1). In this example the factor income components correspond to components of the functional distribution of income. In another example family income may come from such sources as industry and agriculture. In short, a components problem is formed once there is a classification of the sources of income. Generally, when there are n families and p income components, the components problem is summarized by:

(10.la) Yi = W + W2 ... + W?; (i = 1, 2, ... ,n)

(l0.lb) Si = Wi + W + ... + W'; (i = 1, 2, .. ,p) (10.lc) s, = Sl + S2 + + Sp; (l0.ld) fi= Si/SY; (10.le) 1 = 01 + (2 + + (P; (lO.1f) yl < Y2 < ... < Yn- In equation (10.la) the total income [Yi] of the ith family has p components. In equation (lO.ld) the values of 4i (i = 1, 2, ... , p) form a system of weights and correspond to the fraction of the ith type of income received by all families. It will be assumed that total family income [Yi] is arranged in a monotonically nondecreasing order as in equation (10.lf).

S31 S52 MODELS OF ADDITIVE FACTOR COMPONENTS

Table 10.1. Numerical Example of the Problem of Additive Factor Components

Family Family Family Family Family Item 1 2 5 4 5 Total

Wage income 3 1 17 15 9 45 Wage income rank 2 1 5 4 3 - Property income 0 0 2 8 25 35 Property income rank 1 2 3 4 5 - Transfer income 8 12 0 0 0 20 Transfer income rank 4 5 3 2 1 - Total income 11 13 19 23 34 100 Total income rank 1 2 3 4 5 -

- Not applicable. Source:Constructed by the authors.

The components problem can be restated in vector notation: (10.2a) Y = W + WI2 + ... + WP, where

(10.2b) Y = (Y1, Y2, ... , Y,n) and [pattern of total income]

(10.2c) Wi = (I W2, . . ., Wi). (i = 1, 2,..., p) [pattern of the ith factor component] Denote the Gini coefficient of Y by G(Y) or G,, and the Gini coefficient of Wi by G(Wi) or Gi. The basic purpose of the approach using factor income components is to investigate the relations between the total Gini [Gb] and the factor Ginis [G,].

Decomposition of G, into Pseudo Factor Ginis

When the total income pattern [Y] is monotonically arranged, a particular factor component [W'] may not be monotonically arranged (see table 10.1). Thus, to see how the earlier analysis can DECOMPOSITION OF G,,INTO PSEUDO FACTOR GINIS 35S contribute to the understanding of the factor components problem, it is natural to define for each factor component a pseudo factor Gini [Os] in which the exogenously postulated characteristic [C] is the total income rank [Xl:

(10.3a) G. = (2/n)ift - (n + 1) /n by theorem 8.3, where

(10.3b) ii = Xw + X2wu+ . .. .+ Xnw, where (i = 1, 2, .. ., n) (10.3c) Xi = i,

(10.3d) w, = WJ/Si, and (10.3e) w' + w2 + ... + wn 1

From the discussion in chapter nine and from theorem 9.1 in particular, it can be seen that the pseudo factor Gini [GE is the net supporting gap [N] when the total income rank Di] is used as a quality characteristic to explain the variation of a factor income component. This definition of the pseudo factor Gini leads to:

THEOREM 10.1. The Gini coefficient is the weighted average of the pseudo factor Ginis, that is:

Gyu= OIGI + 02G2 + ... + OpGr, where the distributive shares Eri] defined in equation (10.1d) are the weights. Proof: By theorem 8.1 (c) the u index of Y is:

U= XIYI+ X2Y2 + ... + X.Yn X r01(W'/S') + 0,(W,/S 2 ) + ... + 0r(Wl'/Sr)]

2 + X2[Al(W2/S') + +2(W22/S ) + * * * + kr(WF2P/S)]

2 + . .. ± X,n[i(Wn/S1) ± ck2(W2/S ) + ... + 0r(Wp/St)]

1[EX1(W1/S') + X2 (W2/sl) + e e ± X(W'/S')]

2 + 2E2 [X1 (W'/S2) + X2 (W2/S2) + ... + Xn(Wn/S )]

+ ... ±+ kE[Mi(Wfp/SP) + X 2 (W2/SP) + * * * + Xn(Wp/Sv) ]

= Ouil + 02u2 + ... + opfp,uby equation (1O.lb), where ai is the pseudo u index of the ith factor component [Wi]. 354 MODELS OF ADDITIVE FACTOR COMPONENTS

Table 10.2. Gini Decomposition by Pseudo Factor Ginis, 1964-72

Model and variable Notation 1964 1966 1968

All households Total Gini G, 0.321 0.323 0.326 Pseudo wage Gini Gw 0.237 0.270 0.293 Pseudo property Gini 0.449 0.410 0.459 Pseudo agricultural Gini Ga 0.354 0.341 0.178 Pseudo miscellaneous Gini Gm 0.256 0.302 0.363 Wage share 0.432 0.476 0.507 Property share 0.240 0.256 0.278 Agricultural share q. 0.275 0.212 0.152 Miscellaneous share 'km 0.052 0.057 0.063 Wage correlation R. = GU,/GW 1.000 1.000 1.000 Property correlation R,, = GT/GT 1.000 1.000 0.997 Agricultural correlation R. = Ga/Ga 0.999 1.000 0.979

Urban households Total Gini G, 0.329 0.324 0.330 Pseudo wage Gini n.a. 0.280 0.273 Pseudo property Gini n.a. 0.419 0.425 Pseudo agricultural Gini Ga n.a. 0.256 0.311 Pseudo miscellaneous Gini Gm n.a. 0.273 0.337 Wage share 0.573 0.593 0.567 Property share 0.323 0.322 0.337 Agricultural share a 0.037 0.022 0.029 Miscellaneous share 'km n.a. 0.064 0.067 Wage correlation Rw = Gw/Gw n.a. 1.000 1.000 Property correlation R, = GW/G, n.a. 1.000 1.000 Agricultural correlation Ra = Ga/Ga n.a. 0.959 0.990

Rural households Total Gini G, 0.308 0.320 0.284 Pseudo wage Gini n.a. 0.187 0.187 Pseudo property Gini GT n.a. 0.332 0.278 Pseudo agricultural Gini Ga n.a. 0.353 0.337 Pseudo miscellaneous Gini Gm n.a. 0.410 0.365 DECOMPOSITION OF G, INTO PSEUDO FACTOR GINIS 355

1970 1971 1972 Notation Mlodeland variable

All households 0.293 0.295 0.290 Total Gini 0.278 0.273 0.260 Pseudo wage Gini 0.428 0.427 0.424 G1r Pseudo property Gini 0.060 0.107 0.106 Oa Pseudo agricultural Gini 0.354 0.301 0.324 G, Pseudo miscellaneous Gini 0.507 0.545 0.590 Wage share 0.256 0.242 0.258 Property share 0.131 0.102 0.103 e, Agricultural share 0.068 0.060 0.050 'kin Miscellaneous share 1.000 1.000 1.000 R. = Gw/GwWage correlation 1.000 1.000 1.000 R,. = GO,/G,.Property correlation 0.910 0.961 0.958 R. = G,/Ga Agricultural correlation

Urban households 0.279 0.279 0.281 Gv Total Gini 0.233 0.240 0.235 Gw Pseudo wage Gini 0.369 0.399 0.387 Gr Pseudo property Gini 0.154 0.247 0.168 Ga Pseudo agricultural Gini 0.329 0.271 0.280 Gm Pseudo miscellaneous Gini 0.602 0.650 0.634 Wage share 0.302 0.268 0.298 Property share 0.029 0.026 0.024 Xv. Agricultural share 0.073 0.058 0.047 'm Miscellaneous share 1.000 1.000 1.000 Rv = GI/GwWage correlation 1.000 1.000 1.000 R, = G,/G, Property correlation 0.885 0.906 0.879 R. = Ga/Ga Agricultural correlation

Rural households 0.277 0.291 0.284 Ga, Total Gini 0.204 0.220 0.238 Gw Pseudo wage Gini 0.359 0.337 0.348 G,, Pseudo property Gini 0.314 0.318 0.298 Ga Pseudo agricultural Gini 0.282 0.396 0.434 G, Pseudo miscellaneous GiDi (Table continues on the following pages) 356 MODELS OF ADDITIVE FACTOR COMPONENTS

Table 10.2 (Continued)

Model and variable Notation 1964 1966 1968

Wage share 0. 0.213 0.202 0.323 Property share ,,. 0.112 0.100 0.099 Agricultural share X 0.647 0.660 0.526 Miscellaneous share Om n.a. 0.039 0.052 Wage correlation R., = G/G,,, n.a. 0.968 0.995 Property correlation R,, = G,./G, n.a. 0.994 1.000 Agricultural correlation R. = Ga/Ga n.a. 1.000 1.000

n.a. Not available. Note: Compare this table with table 3.2 in chapter three. Sources: Calculated from DGBAs, Report on the Survey of Family Income and Expenditure, 1964, 1966, 1968, 1970, 1971, and 1972.

Thus the Gini coefficientof total income [Y] by theorem 8.1 is:

GD = (2/n) uy - (n + 1) /n

= (2/n)E[1fl + 'k2U2 + .. . + pp] -(n + 1)/n

= 01E(2/n)fzi - (n + 1)/n] + 0 2 [(2/n)fi2 - (n + 1)/n]

* ... ±+ [(2/n) p - (n + 1)/n] + 4l (n + 1)/n

* 02(n + 1)/n + .. . + op(n + l)/n - (n + 1)/n

= 4P1G1 + 22kG2 + . . . + ArGr by equations (10.3a) and (10.le). This completes the proof. In the model of additive factor components, there is a natural interpretation of the pseudo Gini coefficient [Gi] as the concentration ratio, which measures the extent to which the ith factor component is concentrated among wealthy families. Despite the attractive- ness of its economic interpretation and the exactness of its decomposition, the pseudo Gini coefficient has not been used much in the empirical work of this volume. The reasons are these. The pseudo Gini coefficient [G] not only differs from Gi, but is in fact a more complicated concept. Although the factor Gini coefficient [GJ] measures the degree of inequality of a factor component by itself, the pseudo Gini coefficient is definable only in terms of the relatedness of the pattern of factor income, given by (WI, W,;, .. , '), EXACT DECOMPOSITION OF G, INTO FACTOR GINIS 357

1970 1971 1972 Notation Model and variable

0.360 0.357 0.423 c. Wage share 0.103 0.122 0.107 (Al Property share 0.487 0.452 0.423 dtJ. Agricultural share 0.050 0.068 0.047 O. Miscellaneous share 0.997 0.998 1.000 R. = 0G, Wage correlation 0.995 1.000 1.000 R,, = G,/GI Property correlation 1.000 1.000 1.000 R. = Ga/Ga Agricultural correlation

to the pattern of total family income, given by (Y1, Y2, ... , Y). Thus, from the substantive economic point of view, the socioeconomic forces determining Gi are very different from those determining Gj. The decomposition equation in theorem 10.1 can nevertheless be applied in empirical work. Using the same set of data as in table 3.2 of chapter three, the empirical decomposition of the Gini coefficient of total family income [G,] into the pseudo Gini coefficients of wage income [GE,J property income [GE], and agricultural income [Ga] is shown in table 10.2. The decomposition of the Gini coefficient is exact for all three models: all households, urban households, and rural households.

Exact Decomposition of Gv into Factor Ginis

For each factor component [Wi] a factor Gini [Gj] and a pseudo factor Gini [GD] can be computed. The correlation characteristic of the ith factor can then be calculated:

(10.4) Ri = GilGi. (i = 1, 2, ... , p) [factor correlation characteristics]

Theorem 10.1 immediately leads to:

(10.5) G, = 0uRiGi+ 0 2R2G2 + ... + 4,REG,. Equation (10.5) will be referred to as the exact Gini decomposition 3S8 MODELS OF ADDITIVE FACTOR COMPONENTS

Table 10.3. Numerical Example of Exact Decomposition of G, into Factor Ginis

Wage Property Transfer Totao Variable Notation income income income income

Factor share Oi 0.4500 0.3500 0.2000 1.0000

Factor Gini G. 0.3912 0.6628 0.6400 - Weighted factor Gini 4,A 0.1760 0.2320 0.1280 - Total Gini G2 - - - 0.5360

Pseudo factor Gini Gi 0.2308 0.6628 -0.5600 - Weighted pseudo factor Gini *.GA 0.1039 0.2320 -0.1120 - Total Gini G" - - - 0.2239

Average contradicting gap6 s, 0.0802 0.0000 0.6000 - Average supporting gapb s+ 0.3110 0.6628 -0.0004 - Factor correlation characteristico Ri 0.5900 1.0000 -0.8750 -

Gini error E - - - 0.3121

Gini decomposition 4.R.Gi;G, 0.1039 0.2320 -0.1120 0.2239

- Not applicable. Source:Constructed by the authors. a. s, = (Gi - G) /2. b. sak = (Gi+ G,)/2. c. Ri = Gi/lG. formula. It shows that three types of factors affect G,,. If an income component is positively correlated with total family income (Re > 0), then this component contributes heavily to total income inequality when the factor income is unequally distributed (indicated by a large Gj) and when the share of this factor is large (indicated by a large Xi). Conversely, when an income component is negatively correlated with total family income (Ri < 0), a large Gi and a large oi indicate that the component contributes to total income equality. Table 10.3 uses figures from table 10.1 to give the values for the factor shares [oi], the pseudo factor Ginis [GJ], the factor Gini COMPUTATION PROCEDURE FOR EXACT DECOMPOSITION 359 coefficients [Gij, the factor correlation characteristics [Ri], and the Gini coefficient of total income [Gj]. Table 10.3 also indicates the decomposition of G, into pseudo factor Ginis according to theorem 10.1 and the decomposition of G, according to equation (10.5). Notice for transfer income that Ri and Gi are negative. Hence a large share of transfer income [0i] and a more unequal distribution of transfer income [Gi] contribute to total income equality.

Computation Procedure for Exact Decomposition

The following values can be computed for an exact decomposition according to equation (10.5):

(10.6a) Gu = (2/n)u - (n + 1)/n, [total income Gini]

(10.6b) Gi = (2/n)ui - (n + 1)/n, and (i = 1, 2, ... , p) [factor Gini]

(10.6c) Gi = (2/n)ui - (n + 1)/n, where (i = 1, 2, ... , p) [pseudo factor Gini]

(10.6d) u, = l(yi) + 2(Y2) + ... nf(yn) for

Yl < Y2 < ... < Yn,

(10.6e) ui = 1(wj') + 2(w,2) + ... + n(w,') for wji< wji,< ... < w;, and

(10.6f) Fti = l(wu) + 2(w') + ... + n(w'), where

(10.6g) (w,, w', ... , w') = (Ws/Si, W /SS, ... I, W /Si). (i = 1, 2, .. p) Notice when the original data are given as in equation (10.1) or (10.2) that a factor component [Wi] may not be monotonically arranged. For the computation of ui and Gi, the elements in (wi, W2 ... I, w') defined in equation (10.6g), which are not necessarily in a monotonic order, must be rearranged into nondecreasing order. That rearrangement is shown in equation (10.6f) by the permuta- 360 MODELS OF ADDITIVE FACTOR COMPONENTS

tion (jl' i2, ... , jn) of the first n integers. For each factor component: (10.7a) Gi = sg++ s,, and (i = 1, 2, ... ,p)

(10.7b) Gi = s+ - s by theorem 9.1. (i = 1, 2, *.* ,p) Consequently, when Gi and G. are first computed, s4+and s, can be computed: (10.8a) St = (Gi +±G)/2; (i = 1, 2, ... ,p) (10.8b) s. = (GI-G6)/2. (i = 1, 2, ... ,p) The values of st and s- are given in table 10.3. For an empirical application, the correlation characteristies R., R,, and R, are indicated for the three models: all households, urban households, and rural households. Together with the factor Gini coefficients G., G,,, and Ga indicated in table 3.2 of chapter three, an exact decomposition of G, can be attempted for all three models according to the basic decomposition equation (10.5). Notice that the factor correlation characteristics [Ri] can be defined by using equation (9.18) and written as:

(10.9) Ri = GilGi= r(wi, X)/r(wi,ri) = (st - s:)/(st± + s). (i = 1, 2, ... ., p) In this expression, r(wz,ri) is the correlation coefficient between factor income fractions [wi] and factor income ranks [ri]; r(wi,x) is the correlation coefficient between factor income fractions [wi] and total income ranks [X]. There thus are two interpretations for the term Ri in the basic decomposition equation: as the correlation characteristic according to theorem 9.2; as the fractional net supporting gap according to equations (9.18a) and (9.18b). In the example in table 10.3, where the Gini coefficient of wage income [Gm] is 0.3912, the average supporting gap [s+]-that is, the variation of wage income that total family income can explain -is 0.3110; the average contradicting gap [s-] is 0.0802. These values lead to a pseudo wage Gini [GE] of 0.2308. Notice that the property Gini [G,-] of 0.6628 is entirely explained by the supporting gap (G = G = s+), indicating that the correlation between total income rank and property income rank is perfect and positive. The opposite is true for transfer income. THE GINI COEFFICIENT UNDER LINEAR TRANSFORMATION 361

The Gini Coefficientunder Linear Transformation

Let the vectors X = (X1, X2, . . . , Xn) and Y = (Y], Y2, ... ., Yn) be nonnegative. X is a linear transformation of Y if there is a linear function: (10.10) x = b + ay, where a and b are not both negative, such that: (10.11) Xi = b + aYi. (i = 1, 2, ... ,n) It is obvious when Y > 0 that the coefficients a and b cannot both be negative if X is to be nonnegative (X > 0). The following means can be defined:

(10.12a) X = (X 1 + X2 + ... + Xn)/n; [the mean of X]

(10.12b) Y = (Y1 + Y2 + ... ± Y.)/n; [the mean of Y]

(10.12c) q5u = (X1 + X2 + ... + X,)/

(Y, + Y2 + . .+ Y,,). In equation (10.12c) , is the ratio of the mean XVto the mean Y. The theorem to be proved in this section is:

TEIEOREM 10.2. If X = (X1 , X2, ... , X,) is a linear transformation of Y = (Y1, Y2, ... , Yn) -that is, if Xi = b + aYi for i = 1, 2, ... , n-then:

(a) G(X) = (a/0ry)G(Y) i.f a > 0, and (b) G(X) = -(a/4.v)G(Y) if a < 0, where i, = X/Y and where G(X) and G(Y) respectively are the Gini coefficients of X and Y. For a geometric interpretation of this theorem, notice that: (10.13a) X = b + aY, 362 MODELS OF ADDITrVE FACTOR COMPONENTS which implies that: (10.13b) (b/X) -1 = -a/0, by equation (10.12c). Because the elasticity of the linear function in theorem 10.2 is: (10.14) (dx/dy)(y/x) = al(xly), it can be seen that a/(X/Y V) = a/O,, is the elasticity of the linear function at the mean point (X,Y). Thus theorem 10.2 states that G(X) can be obtained from G(Y) by multiplying G(Y) by the elasticity at the mean point (X,Y). Theorem 10.2 can be proved as follows:

Proof: Assume that Y1 < Y2 < ... < Yn. If a > 0 and X1 > X2 > ... > X, then by theorem 8.1:

u. = (1X±+ 2X2 ±+. . . + nX.)/nX

= [(b -+ aYi) + 2(b + aY2 ) + ... + n(b + aY.)]/nX = b(l + 2 + ... + n)/nX + a(nY/nX)u,, by theorem 8.1 = (n + 1)b/2X + au.,,/, by equation (10.12c). Thus by theorem 8.1:

G(X) = (2/n)[(n + 1)b/2X + au,/O)]- (n + 1)/n = (a/.,,) (2/n)u% + b(n + 1)/ni- (n + 1)/n

= (a/X) (2/n) u + E(n + 1)/n](b/lf - 1)

= (a/O..) E(2/n) -(n + 1) /n] by equation (10.13b)

= (a/lov)G(Y).

This proves the case for a > 0. If a < 0 and Y1 < Y2 < ... < Y, the values of Xi are in a reverse monotonic order X1 > X 2 > ... > X,. The above proof implies that G(X) = (a/q.,)G(Y) by theorem 8.3. Now, however: O(X) = -G(X) by theorem 8.4. This completes the proof. A positive coefficient a in equation (10.10) gives:

THEOREM 10.3. If X = (X1 , X 2, ... , X,,) is a linear transformation of Y = (Y 1 , Y2, . .. , Y.) with a positive coefficient a > 0 LINEAR MODEL OF ADDITIVE FACTOR COMPONENTS 363 in x = b + ay, then: (a) G(X) > G(Y) if and only if a/oz,, > 1 or b < 0, and (b) G(X) < G(Y) if and only if a/+,,? < 1 or b > 0. Proof: From theorem 10.2 it can be seen that G(X) Ž G(Y) if and only if: a ; 0zv = X/Y = (b + aY)/Y by equation (10.13a), or aY t b+ aY. This completes the proof. The theorem essentially states that b is negative when the function defined in equation (10.10) is elastic at the rnean point (X,Y), and that b is positive when the function is inelastic at the mean point (X,Y). The rest of the proof directly follows from theorem 10.2.

Linear Model of Additive Factor Components

Now consider a special case of the additive factor-components problem defined in equation (10.1). For this special case, postulate:

(10.15a) wi = bi + aiy, where (i = 1, 2, ... , p)

(10.15b) a + a 2 + ... + a = 1 and

(10.15c) bi + b2 + ... + bp = 0,

such that the ith factor component [Wi = (Wj, W, . . , W) ] is a linear transformation of the total income pattern EY = (Y1 , Y2, ... > Yn)] according to the ith linear function in equation (10.15a). In other words:

(10.16) Wi = (Wi, Wi, . . .w, I) = (bi, bi, .. ,bi) + ai(Yi, Y2, ... Y). (i = 1, 2, .. p) Notice when the restrictions of equations (10.15b) and (10.15c) are postulated for ai and bi that:

(10.17) Y = WI + W2 + .. + Wn so that Y is the sum of all values of Wi, as in equation (10.2). 364 MODELS OF ADDITIVE FACTOR COMPONENTS

This model will be referred to as the linear model of additive factor components. It is a special case of the general model defined earlier. Notice in equation (lO.i5a) that some values of as may be negative. But when ai is negative, bi must be positive (see equation [10.10]). Thus with no loss of generality the pairs (ai,bi) can be classified into three types of case. For a type one component:

(10.18a) as > 0 and bi < 0; (i = 1, 2, ... , q) for a type two component:

(10.18b) ai > 0 and bi > 0; (i = q + 1, q + 2, . ,t)t. for a type three component: (10.18c) ai < 0 and bi > 0. (i = t + 1, t + 2,...,) Let G, be the Gini coefficient of Wi and G, be the Gini coefficient of Y. Applying theorem 10.2 gives: (10.19a) Gi = (aj/1j)G,, or aiGy = iGi, and (i = 1, 2, . ,t) (10.19b) Gi = -(ai/4j)G,, or aiG, = -OiGi, (i= t+ 1,t+2, ... ,n) where 1 0, ... p, are the distributive shares defined in equation (10.ld). When all the romanized terms in equations (10.19a) and (10.19b) are added, equation (10.15b) implies that:

(10.20a) G, = H1 + H2 - Hs, where

(10.20b) H1 = 41G1 + 02G 2 + ... ± qGq, Etype one components]

(10.20c) H2 = .q+,Gq+ + 0k+q2Gq+2 + ... + 0,Gt, and [type two components]

(10.20d) H3 = ¢o+lGt+, + (t+2Gt+2 + .+. . + [type three components]

Equation (10.20a) is an exact decomposition of G, for the linear model of this section. Notice that this decomposition equation is a MONOTONIC MODEL OF ADDITIVE FACTOR COMPONENTS 865 special case of the general decomposition equation (10.5). For this special case, theorem 10.3 further implies that: for type one income:

(10.21a) Gi 2 Gv, and (i = 1, 2, .. , q) for type two income: (10.21b) Gi < G,. (i = q + 1, q + 2, . ,t) Thus, in the linear model, a type one factor component is distributed more unequally than Y. A type two factor component is distributed more equally than Y. A type three factor component contributes more to income equality the more unequally it is distributed-that is, when Gi increases, GDdecreases.

Monotonic Model of Additive Factor Components

Postulate for the generally defined model of additive factor components in equation (10.1) that every factor component [W; = (Wli, W2, . . , W') ] satisfies: (10.22a) wi < W_ < ... < W, or [monotonicallynondecreasing conditions] (10.22b) Wli> Wli> ... 2 Wi-. [monotonicallynonincreasing conditions] The linear model obviously is a special case of this monotonic model. When the total incomepattern [Y] is monotonicallynondecreasing, a type one or type two incomeobviously is monotonicallynondecreasing;a type three incomeis monotonicallynonincreasing. Applyingequations (9.17a) and (9.17b) to Wi in the monotonic modelgives: (10.23a) Gi = Gi, when Wi is in a monotonicallynondecreasing order, and: (10.23b) Gi = -0i, when Wi is in a monotonicallynonincreasing order. In the first case the factor Gini coefficientequals the pseudo factor Gini coefficient. In the secondcase it equalsthe negative value of the pseudo 366 MODELS OF ADDITIVE FACTOR COMPONENTS factor Gini coefficient. Substituting equations (10.23a) and (10.23b) in the equation of theorem 10.1 gives:

THEOREM 10.4. In the monotonic model:

G-= U1 - U2, where

(a) Ul = klG1 + q 2G2 + ... ±+¢tGt and [monotonically nondecreasing Wi]

(b) U2 = Ot+1Gt+l + O+2Gt+2 + ... + O.Gn. [monotonically nonincreasing Wi] In comparison with the general decomposition equation (10.5) it can be seen in the monotonic model that all values of Ri, the correlation characteristic, equal 1 or -1. Furthermore the decomposition equation in the linear model (10.20) is a special case of theorem 10.4. In other words, the linear model is a sufficient, but not a necessary, condition for deducing Ri to be 1 or -1. The monotonic model of this section is useful for empirical application because, when total income is monotonically arranged [Y1 < Y2 < ... < Yn]J it can often be assumed, as a first approximation, that all factor components [Wi] satisfy the monotonic conditions of expression (10.22). The primary advantage of the monotonic model is the simplicity that accrues to theoretical analysis when all correlation characteristics are assumed to be 1 or -1. Consider the following numerical example:

(10.24a) (Y1, Y2, Y3) = (20, 30, 50), G, = 0.2; (10.24b) (W1, W2, W3) = (10, 24, 46), G. = 0.3,

Co = 0.8, (W1 < W2 < W3);

(10.24c) (1n, 72, Ir3) = (10, 6, 4), G, = 0.2,

0, = 0.2, (Xl > Ir2> m3);

(10.24d) (Yr, Y2, Ya) = (WV, W2T)W I+ (wi, Tr2, Tr3); (10.24e) G, = 4.G, - 0,WG,= (0.8) (0.3) - (0.2) (0.2) = 0.2. Notice that the two factor components are not linear transforma- tions of (Y1, Y2, Y3). Yet theorem 10.4 can be applied because the monotonic conditions are satisfied. Notice also that a minus sign is attached to the component (rl, T2, r3) because it is in a monotonically nonincreasing order. LINEAR APPROXIMATION OF FACTOR COMPONENTS 367

Linear Approximation of Factor Components

Suppose that Y and Wi (i = 1, 2, .. . , p) are interpreted as original data and given as in equation (10.2) such that some Wi is not a linear transformation of Y. In this section the purpose is to investigate the construction of approximated factor components [Wi = (WL W2, .. ., Wi) (i = 1, 2, ... , p)] which satisfy the following conditions:

(10.25a) Y = Wl + W + .. . WP, and

(10.25b) 'i = (Wli + W ± ... + Wi)/nY

= ( +lit+W2± . .. ±IVD/rt, (i = 1, 2, ... ,n) where Wi is a linear transformation of Y according to:

(10.25c) wi = bi + aiy, (i = 1, 2, ... , p)

(10.25d) Q1+ Q2+ + Qp= 1,

(10.25e) 61 + b2 + ... + bp = 0, and

(10.25f) Wj = bi + diFY. (i = 1, 2, .. ,p; j= 1, 2, .. ,n)

The vector Wi constructed in this way will be referred to as a linear approximation of Wi. Condition (10.25a) states that Y, interpreted as original data, is the additive sum of the linear approximations of the factor components [Wi]. This condition is ensured by the fact that Wi is a linear transformation of Y with the conditions postulated in equations (10.25d) and (10.25e). Condition (10.25b) states that the factor share [0i], originally defined for Wi, remains unchanged when Wi replaces Wi. With such an approximation, the original additive factor-components problem, which in equation (10.2) is stated as: (10.26) Y = W±+ W2 + ... + WP, is now replaced by a new additive factor-components problem through a linear approximation. The primary advantage of the formulation of this new problem is the theoretical simplification the linear approximation brings about. If G(Wi) is the Gini coefficient for the approximated factor com- 368 MODELS OF ADDITIVE FACTOR COMPONENTS ponents (W'), equation (10.20a) immediately implies that:

(10.27a) G, = fl'1 + 22 - Th, where (10.27b) 121 = 40,G(W')+ 02G(W2) + ... + OG(W-) for type one incomes satisfying di > 0 and bi < 0;

(10.27c) -22 = 0,+ 1G(WF+l) + 0+2 G(*jJf+2) + ... + OsG(#7V) for type two incomes satisfying di > 0 and bi > 0; and

(10.27d) A, = 0+ 1,G(Wft+I) + k,+2G(V'+2) + ... + 0,G(*-J) for type three incomes satisfying di < 0 and bi > 0. Equation (10.27a) is comparable to the general decomposition equation (10.5) when the correlation characteristics [Ri] are 1 or - 1. Furthermore the classification of income into types one, two, and three, hitherto definable only in the context of the linear model, becomes applicable. The new decomposition problem thus becomes simpler and wealthier in economic content. To proceed with the construction of Wi, the linear function in equation (10.25c) is treated as a linear regression equation in which the parameters ai and bi are estimated from the original data for Y and Wi (i = 1, 2, ... , p) by the method of least squares. Con- dition (10.26), a property of the original data, ensures that equations (10.25d) and (10.25e) are satisfied when the method of least squares is used. When these regression functions are constructed, the estimated factor components [EW (Wi W,..., W) (i = 1, 2, p) ] are obtained by substituting Yi in the regression equation (10.25f). To prove equation (10.25b) it can be seen for the ith regression equation that:

(10.28a) oi = (p, 92,* * *, °n)

= (Wi, Wi, * . ., Wi) - (, W;, . . .W,i); (10.28b) lkWi, ... , n)

= (bi, bi, . . ., bi) + ai(YI, Y2 , . . ., Yn) by equation (10.25f);

(10.28c) Of+62 + *.+ o °=0;

(10.28d) Wli + W2 + . . . + W'= W + 2 + * . . + nW =ai(Y, + Y2 + . .. + Y.) + nbi. LINEARITY ERRCR 369

In equation (10.28a) Oi contains all the deviations [EO (j = 1, 2, .n) ] of W' from the estimated W,. The least-squares method of estimation implies that the sum of all deviations is zero [equation (10.28c) ]. Summing both sides of equation (10.28a) directly leads to equation (10.28d) which shows that the sum of all elements in Wi, the original data, is the same as the sum of all elements in the pattern of approximated factor incomes [Wi]. Thus 4i remains unchanged.

Linearity Error

When the original data are given for Y and Wi (i - 1, 2, ... p), the method of linear approximation can be used only when every Wi approximately is a linear transformation of Y. In computing the regression coefficients [4i and bi] in equation (10.25c), the correlation coefficientsshould also be calculated:

(10.29) ri = r(Y,Wi). (i = 1, 2, ... , p) [correlation coefficients] The values of ri give an indication of how close the linear approximation is. It is recommended that the method of the preceding section be used only when all absolute values of ri are sufficiently close to 1-that is, only when all values of Wi are nearly perfectly correlated with Y, whether positively or negatively. When this condition is not met, the following approximation formula can be defined by replacing every G(Wi), the factor Gini of the approximated factor component, by G(Wi), the true factor Gini:

(10.30a) ,, = H1 + H2 - 1, where 2 (10.30b) 1T = OG(W') + 02G(W) + ... + .G(Wq), 1 2 (10.30c) 122 = 0q+G(Wq+ ) + O,q+2G(W1 ) + ... + OtG(Wt),and 1 2 (10.30d) 123 = 0,+1G(Wc+) + Ot+2G(W'+ ) + ***+±pG(WI). When this approximation formula is used, an error term EJ] is involved. It is the difference between G,, as defined in equation (10.27), and U,,:

(10.31a) J = U,, - Gv, = JI + J 2 - J3, where

(10.31b) Ji = sldl + 2Ad2 + *.. + dSd, 370 MODELS OF ADDITIVE FACTOR COMPONENTS

(10.31c) J2 = ,+f1d,+ + 0,+2d,+2+ + q¶tdt, and

(10.31d) J3 = 0,+1d,+ + 01+2dt+2 + ... + ,dp, where (10.31e) di = G(Wi) - G(fVi). (i = 1, 2, .. , p) In equation (10.31e) di is the difference between the Gini coefficient of the true factor component and that of the approximated factor component. Notice in equation (10.28a) that the difference between Wi and Wi is Oi.When the absolute value of the correlation coefficient Eri] is close to 1, 9i is close to a zero vector, leading to the fact that di is close to zero. By comparing equation (10.30) and theorem 10.4, it can be seen that the approximation formula can be used even when the absolute values of the correlation coefficients [ri] are not close to zero. In other words, the fact that they are close to zero is a sufficient, but not a necessary, condition. In the monotonic model, G, is equal to G. Hence the linearity error vanishes-that is, J = 0-even though di, d2, . . ., d, may not vanish. [For a numerical example see equation (10.24).] Thus it is recommended in attempts to apply the linear model to empirical work that checks be made to ensure that the following conditions are fulfilled: (10.32) j ri I = I r(Y, Wi) I 1. (i = 1, 2, . . ., p) In words, the linear correlation coefficientbetween Wi and Y should be close to 1 or -1.

Approximation of the Monotonic Model

Supposethat Y and Wi (i = 1, 2, ... , n) are given as in equation (10.2) and that the monotonic conditions are only approximately satisfied. If the monotonic model is to be used, the equation of approximation is:

(10.33) G, = U1 - U2, where U, and U2 are defined as in theorem 10.4. The difference between G, and G2, as defined in the exact decomposition equation (10.5), is the Gini error term: A (10.34a) E = G - G,= E1 - E2, where APPROXIMATION OF THE MONOTONIC MODEL 371

(10.34b) E1 = 5igt+ 02g2 + ... + kogt2 0 for 0 < Ri < 1, and

(10.34c) E2 = ot±lgt+i + ot+2gt+2 + * ±+ o,gP > 0 for -1 < R• < 0, where

(10.34d) g, = Gj(1 - Rj) and (i = 1, 2, ... , t)

(10.34e) gi = Gi(l - Ri). (i = t + 1, t + 2, ,p)

The term El includes all components [Wi = (Wi, W2, ... , W')] for which Ri is positive. This condition is interpreted as approximately satisfying the monotonic increasing condition [Wl' < W2' < ... < WW]. Similarly the term E2 includes all Wi for which Ri is negative. This condition is interpreted as approximately satisfying the monotonically decreasing conditions [Wi > W2' > ... > Wi]. It is easy to show that El and E2 in equations (10.34b) and (10.34c) are nonnegative. The Gini and pseudo Gini coefficients of a factor component EW?] may be written as they are in equations (10.7a) and (10.7b): (10.35a) Gi = st + s; (i = 1, 2, ,p) [factor Gini] (10.35b) G=s+s(i= 1, 2, . ,p) [pseudofactor Gini] When the total income pattern [Y] is monotonically arranged [Y1 < Y2 < ... < Yn] for a particular factor component [W' = (Wli, Wi, , Wi)], the average supporting gap [st] is the sum of all such terms satisfying (W' - Ws) > 0 for u > v. In other words, if the total income is higher (Yu > Y~), the factor income is also higher (W' > WI). Conversely the contradicting gap [s- ] includes all terms such that the factor income is lower (Wu < W,) if the total income is higher. Equations (10.34d), (10.34e), (9.12a), and (9.21b) give:

(10.36a) gi = 2s- (i = 1, 2, ... , t) when W, < W' < ... < W' is approximately satisfied and: (10.36b) gi = 2s+ (i = t + 1, t + 2, ... ,n) 372 MODELS OF ADDITIVE FACTOR COMPONENTS when Wi > Wi > ... > Wi is approximately satisfied. The fact that s- and s+ are nonnegative implies that E1 and E2 are nonnegative, as was to be demonstrated. Furthermore the underlying nature of the error terms is now known. For E1 the error is traced to the violation of monotonically increasing conditions. For E2 the error is traced to the violation of monotonically decreasing conditions. Because E is the difference between two nonnegative terms E1 and E2 , it can be seen that G, defined in equation (10.33) can either underestimate or overestimate the true G,. If all values of Ri are positive, then E2 vanishes and G, always overestimates G,. This condition can be stated as: THEOREM10.5. If all factor correlation characteristics are positive- that is, if Ri > 0 for i = 1, 2, . .. , p-then the error of estimation [E] defined in equation (1 0.34) is:

E = El = 2 (qis- + 02s2 + .. + fxsp,) 2 °

Hence Gy = OIG1 + k2G2 + ... + G always overestimates Gy. Furthermore E is twice the weighted sum of contradicting gaps. When the monotonic model is to be used for empirical work, equation (10.34) suggests that the following conditions should be verified after the correlation characteristics [Rij are computed: (10.37) 1 Ri I -1. (i = 1, 2, ... ., p) In words, the absolute values of all Rf should be close to 1 to ensure that the monotonic conditions are approximately fulfilled. CHAPTER 11

Applicationsand Extensions of the Models of Decomposition

THE CONSTRtUCTION OF A GENERAL MODEL of additive factor components in chapter ten led to the exact decomposition equation (10.5). Construction of the monotonic model, a special case of the general model, led to the exact decomposition equation in theorem 10.4. Construction of the linear model, a special case of the monotonic model, led to the exact decomposition equation (10.20). These three models can be used both for theoretical purposes and for empirical applications. The general model of equation (10.5) is most useful for empirical applications because of its generality. Precisely for that reason, however, the monotonic model or the linear model may be preferred for theoretical purposes. If there are a priori reasons, based on economic theorizing, for assuming that the monotonic conditions of expressions (10.22a) and (10.22b) are fulfilled, the monotonic model should be used. Similarly, if there are a priori reasons for assuming that the strong linear conditions of equation (10.16) are fulfilled, the linear model should be used. The monotonic model is less complicated than the general model, because the correlation characteristics can be neglected as a first approximation. The linear model can, in addition, identify three different types of income- types which help in reasoning about the distribution of income. In reality, the monotonic and linear conditions can only be approximately fulfilled. Thus the exact monotonic and linear models are used for theoretical purposes; the approximation models, for empirical work.

573 374 APPLICATIONS AND EXTENSIONS OF THE MODELS OF DECOMPOSITION

Remarks on Chapter Three

The approximation of the linear model was applied in chapter three. Because of the aggregated data, the conditionsof equation (10.32) were judged to be fulfilled: I ri I = I r(Y, Wi) I 1 (observe the values of r,, r., and r, in table 3.3). For the empirical applicationin that chapter,there was no type three income(observe that the values of a., a,, and a. are positivein table 3.3). Thus the terms H3 and J3 respectively vanish in the approximation equation (10.30a)and the error equation (10.31a),which reduce to: (11.la) u = 1i + 2, and

(11.lb) J = JL + J 2 . The value of J is denoted by Uin table 3.2 of chapter three. Notice that because the linear conditionsare judged to be fulfilled,the values of 0 are quite tolerable. The overestimationof the true Gv by G,, which the positivevalues of 0 in table 3.2 indicate, is suggested by theorem 10.5:G, -G = X 0. How do the formulationsof chapter three relate to those presented in chapter ten? In the theoretical derivation of chapter three, equation (3.3b) is a special case of equation (10.30a): that is, Gu = ¢OwG.+ -GT - OkNGNis a special case of v,,= fll + f12 - 12g.(Notice that the term kNGN corresponds to a type three income.) Equation (3.5a) is a specialcase of equation (10.25f):that is, Wi = b. + aiY is a specialcase of W# = bi + diY,. The definitionof Gu in equation (3.8b) is the same as in equation (10.30):that is, Gu = Hi + H2 - H3 is the same as G,v= i21+ 122- 123.Nevertheless 0, which correspondsto J in equation (10.31), was not explicitlydis- cussedin chapterthree. Theorem3.1 corresponds to equation(10.27): that is, Gu = 121+ 122 - 3. Theorem3.2 correspondsto equation (10.19): that is, G(1i) = (ai/lo)G, = Gi for type one and type two incomes,and G(47i) = - (ai/¢)G, = Gi for type three income. The statements in equations (3.12a) and (3.12b) are proved by equation (10.21):that is, Gi 2 Gufor type one income,and Gi < Gu for type two income.Equations (3.14a) and (3.14b) are suggested by theorem 10.5:that is, when there is no type three income,G" = k1G1 ± t2C2 + .O.. + 0Gr - 0,where 0 > 0, is suggestedby Gv = REMARKS ON CHAPTER SIX 375

0,G, + 02G2 + ... ± 4yG,, where GQoverestimates GQby an amount equal to the error term E.

Remarks on Chapter Six

Equations (6.3a) and (6.3c) of chapter six stated that:

(11.2a) V = C=+ C2 + C3 + S and [expenditure model]

(11.2b) Y= V+ T1 + T2. [tax model]

In the expenditure model the pattern of income after tax [V = (V 1, V2, ... , VT)] is the sum of three consumption components ECi = (Cil, C6, . . ., Cin) (i = 1, 2, 3)] and a savings component ES = (si, s2, ... , s)]. In the tax model the pattern of income before tax EY = (yl, Y2, . . ., y,)] is the sum of V and the patterns of direct tax payments ET1 = (tll, t12, . . . , tj, )] and indirect tax payments ET2 = (t2l, t22, . . . , 12)]. For these two models the exact decomposition equation (10.5) was applied: G, = Z &iRiGi Esee equations (6.4a) and (6.4b) in chapter six]. The tax model is a good example of the way sound economic reasoning should guide the choice among decomposition models. When total income before tax is monotonically increasing E1¾ < Y, < ... < Y.], any reasonable taxation system should approximately satisfy the conditions that V, T1, and T2 also are monotonically increasing-conditions described as "no reversal of rank" and "minimum progressiveness" in equation (6.8) of chapter six. Thus confidence in this reasoning should have led to the choice of the monotonic model, not the more complicated general model. As it turned out, the accuracy of exact decomposition associated with using equation (10.5) is spurious because all the correlation characteristics [Ri] are close to 1, as would be expected in the first place (see the values of R., R', and R' in table 6.3 of chapter six). In the expenditure model, whether Ci should be monotonically increasing or decreasing is a matter of well-known theoretical speculation in the economic theory of consumption. The pattern of consumption ECi] is expected to be monotonically increasing if the 376 APPLICATIONSAND EXTENSIONS OF THE MODELS OF DECOMPOSITION

commodity is a noninferior good; it is expected to be monotonically decreasing if the commodity is an inferior good. For this model it turns out that the correlation characteristics [Ri] also are close to 1 (see the values of R', Re, R3, and R. in table 6.2). Nevertheless the general equation (10.5) was used in chapter six, as it should be in such cases, because the strength of those correlations was uncertain until the values of Ri were calculated.

Additive Factor Components and Growth Theory

The models of additive factor components have been abstractly constructed to emphasize that these models can be applied to many problems once there is a classificationof the sources of income. In a theoretical application, the models must be combined with additional theoretical notions, economic and noneconomic, to increase the understanding of the social and economic forces that determine the equity of family income distribution. When adopting such an approach, certain behavioristic assumptions usually must be added to the framework of additive components. The analysis of equity in relation to growth in chapter three is an example of such an approach. But in that chapter the linear model was used as a first approximation: G,, = qwG. + ,G,, - 0. What if the basic decomposition equation (10.5) had been used instead? What would have been the added theoretical requirement associated with such a generalization? To illustrate with the urban family case of chapter three: (11.3) G,, R=wR.G, + R.,,G,r, where fw + + = 1. Equation (11.3) decomposesC,G into the wage income effect [R.0 G.] and the property income effect [Rr+pGr. The decomposition now is exact. This exactness appears to be an advantage, because it now is unnecessary to worry about an error term in empirical applications. That advantage is not gained, however, without a cost. The theoretical requirement becomes greater because of the appearance of the correlation characteristics [RW,and R,.] in equation (11.3). When these variables are functions of time, differentiating equation (11.3) gives:

(11.4a) dGy= Bo + Do + Ro, where ADDITIVE FACTOR COMPONENTS AND GROWTH THEORY 377

(1 1.4b) Bo = R.or dG + R+r r dGt (liAb) BO = ~~~dt dt EfactorGini effect]

(11.4c) Do = (RtoG. - RiOG) d-', and

Uunctionaldistribution effect] dR_ (11.4d) R° = dt+G. dt+

Ecorrelationeffect] Notice that the terms Bo and Do are direct generalizations of the factor Gini effect [B] and the functional distribution effect [D] of equation (3.16) in chapter three. The term R° is a newly added correlation effect. It indicates the impact of the variation of the correlation characteristic on total income inequality. It essentially captures the variations of the ways in which wage and property income are correlated with total family income: that is, the extent of exceptions to the rule that wealthier families tend over time to receive more wage and property income than poorer families. This simple example shows that at least three types of forces can affect G, in the process of growth. The endeavor to link growth theory with income distribution theory can proceed at the aggregate or disaggregate level. The framework of reasoning provided by equation (11.3), or equation (3.16) in chapter three, aims to link them at the aggregate level and to take advantage of the knowledge accumulated in the more developed branch of development theory. A good example of this link is the functional distribution effect; another is the reallocation effect in the more general a.ll-households model. These effects constitute the focal points of analysis of aggregate growth theory in a dualistic economy and can now be incorporated into the framework of FID analysis. It should be noted that very little is inductively known about Ro. Even less is known about a positive behavioristic theory of R°. Thus, by focusing on the special case in chapter three and omitting RO in the framework of reasoning, heavy costs are not incurred because not much is to be gained by including R°. This is not to deny that future advances in understanding R° would be helpful. 378 APPLICATIONS AND EXTENSIONS OF THE MODELS OF DECOMPOSITION

The obvious advantage of theoretical simplicity in the special case must be weighed against the disadvantage of imprecise results traceable to the omission of R°. When aggregated data are used, as in the analysis in chapter three, O/G, is observed to be uniformly less than one percent. Thus the precision of analysis is not impaired by the use of the approximation formula. In fact, the use of equation (11.3) instead of Gy = ±>G+ ,G,. - 0 would have led to an expen- sive search for spurious accuracy traceable to a factor [RO] about which not much is known. By constructing a number of abstract models of additive factor components as frameworks for theoretical reasoning and empirical analysis, it has been shown that the choice of appropriate models is guided not only by the availability of statistical data, but by the complementary theoretical inputs which are currently or potentially available.

Income Components with Observation Error

In economic applications total family income [Yi] may be the sum of several components and an observation error [Di]. Thus: (11.5a) Yi = Wii + W2i+ ... + Wit + 6i; (i =1, 2, *,n)

(11.5b) 61+ 62 +* + a =0;

(11.5c) s = Y + Y2 + ... Y = S±+ S 2 + *+ S; (11.5d) Si = Wl' + W,' + ... + Win. (i = 1, 2, . ,p)

In vector notation let 6 = (d1, a2, . . ., an). Then: (11.6a) Y = Wl + W 2 + . . . + WP ±,+ where

(11.6b) a = (a1, 62, ...* * a Notice that the sum of all elements in a is zero by construction. All other vectors-that is, Y and Wi (i = 1, 2, ... , p)-are assumed to be nonnegative. Thus the only difference between equation (11.5) and the components problem introduced at the beginning of chapter ten is that one "factor component" may have negative entries: a. Such a situation may arise, for example, when Y and Wi are independently estimated in empirical work. The Gini coefficients G, and Gi (i = 1, 2, ... , p) can be de- INCOME COMPONENTS WITH OBSERVATION ERROR 879 fined as before. But a Gini coefficient cannot be defined for i because it contains negative entries. To construct a decomposition equation, first construct a system of weights and define a weighted observation error, 6, in the following manner: (11.7a) ji = i/g, where (i = 1, 2, , n) (11.7b) g = 1 + 2 + . .. + n = n(n +1)/n,

(11.7c) 6 = jlbl + j22± .. + nn, and

(11.7d) A = 6/Y, where

(11.7e) Y = (Y 1 + Y2 + ... + Y.)/n and

(11.7f) il + i2 + . . . + jn = 1. Thus (ji, j2, ... , jn) are the "rank weights"; 6 is the rank-weighted observation error; and A is a expressed as a fraction of the mean income of all families.

THEOREM 11.1. G, = 0,G, +± 2G2 + ... + 0,0p + (n + 1) A/n, where A = / Y.

Proof: UD = (1/s) 2Yi Xi = (1/s,) E Xi(Ww + Wi + Wij + bi) by equation (11.5)

=(Sl/S) (E XiWV/s 1) + (S2/Sy) (E XiXW/s 2 )

+ ... + (sp/sS) (E XiW-V/s) + (1/sn) E Xiai 4 - Olfl + 42U 2 + . . . + ),ii + J, where

J = (1/sy) EXi5i = (S./Sy) (X51a/S. + X262/S& + . + X.5/.S.)

= [n(n + 1)/2sj[ji5, + j262 + ... + ji] by equations (11.7b) and (11.7c) = (n + 1)a/2Y = (n + 1)A/2. Hence:

Gv= (2/n)u% - (n + 1) /n

= (2/n)[U 19i + 2u2 + . . . + opiip + (n + 1)A/2- (n + 1)/n

= 0'101 + k2G2 + . .. .+ tpGp+ (n + 1) A/n. This completes the proof. 380 APPLICATIONS AND EXTENSIONS OF THE MODELS OF DECOMPOSITION

Based on theorem 11.1, equation (10.5) can be modified as:

(11.8a) G, = 4O1RG1 + 0 2R2G2 + ... + 4,RpG, + (n + 1)A/n, where:

(11.8b) Ri = ai/Gi and (i = 1, 2, ... , p)

(11.8c) A = S/ = (ji&, + j2a2 ... + jj.)/Y, where (11.8d) ji = 2i/n(n + 1). Theorem 11.1 is a direct generalization of the special case of equation (10.5).

Family Income with Negative Components

In empirical reality the net income of a family may have a negative component. For example, although gross income has such positive components as wage income and property income, tax payments must be subtracted from gross income to obtain net family income. The following equations formulate this problem conceptually:

(11.9a) Wi = col(Wl, W2, . ,. . Wn) > 0; (i = 1, 2, . . ., p)

(11.9b) Zi = col(Z,i, Z2i, . ., Z') 2 0; (i 1, 2, . . ., q)

(11.9c) 6, = col(i1, 62, . .., an); ( Ei = 0)

(1 1.9d) Y = Wl + W2 + . + .....WP - Z' - Z2 ...... + 6, _Z"

= col(Yl, Y2 ,. ... Yn) > 0; (11.9e) X = Y +Z' + Z'+ ...... + Zq= TV'+W2 + +...... +WP + 3

col (XI, X2 , .. ., X.) 2 0. Thus Wi stands for the ith positive income component; Zi for the ith negative income component. Net family income is Y; gross family income is X. As in the preceding section, 6. stands for a column vector containing the elements 6i with a zero sum. It is assumed that gross incomes are arranged in a monotonically increasing order:

(11.10) XI < X 2 < ... < Xn. The purpose of the analysis is to find out the causation factors FAMILY INCOME WITH NEGATIVE COMPONENTS 381 that explain G,, the inequality of net income. Equation (11.9d) shows that this problem can be solved by investigating two components problems: (11.11a) X = Y + ZI + Z2 + + Z9; (11.l1b) X = WI +W' + ... + WP +6 To apply equation (11.8) to these problems, the terms oi, Ri, and A must be defined. For fi, define:

(11.12a) X = (Xi + X2 + ... + X.)/n, (11.12b) 2i = (Zli+ Z2 + .. + Z') /n, (i =1, 2, * ,q)

(11.12c) W i=(Wl+ W2+ ...... + W')/n, .. (i =1, 2, ... ,p)

(11.12d) Y (Y1 + Y2 + ... + Y.)/n;

(11.13) X = Y + (Z1 + 2 + ... + Zq) by equation (11.9e)

= Wl+fV2+ ... +Wp, by equations (11.9e) and (11.9c); (11.14a) 01,= Y/X,

(11.14b) CS= Z4/X, (i = 1, 2, ... , q)

(11.14c) '° = Wi/X, (i = 1, 2, ... , p)

(11.14d) Oi= 0 = Zi/Y, (i = 1, 2, ... , q)

(11.14e) 6, = d,/4v = Wi/Y; (i = 1, 2, . ,p)

(11.15a) 4, -l+ +± + .2. . + 4 = 1 by equation (11.12b),

(11.15b) + ++w *w+ ... + ow = 1 by equation (11.12b).

In equation (11.12) the means are defined for all the column vectors of equation (11.9e), leading to the equalities in equation (11.13). The relative shares of the two components problems in equation (11.11) are defined in relation to these means. Observe that 0b, is net income as a fraction of gross income; 4, is the ith income component as a fraction of gross income; 0$ is the ith payment as a fraction of gross income. In equation (11.14) the income and payment components are expressed as a fraction of net income: O, and V,. To apply equation (11.8), the following must also be 382 APPLICATIONS AND EXTENSIONS OF THE MODELS OF DECOMPOSITION defined:

(11.16a) G. = G(X), (11.16b) G, = G(Y),

(11.16c) G- G(Zi), (i = 1, 2, , q)

(11.16d) G.= G(W9); (i = 1, 2, ... , p) (11.17a) ay (y), (11.17b) G= (i,(i =1, 2, . ,q)

(11.17c) Gs = G(Wi); (i = 1, 2, . . ., p) (11.18a) R, = 6.1Gy,

(11.18b) R= GJGs, (i = 1, 2, ... , q)

(11.18c) R,' = G, ; (i 1, 2, ... , p)

(11.9) A (jll + j262 + ... + j,bn)/X by equation (11.8c). In equation (11.16) G, is the Gini coefficient of gross family income; G,, of net family income; GT, of the ith income component; G., of the ith payment component. The pseudo Gini coefficients are defined in equation (11.17). Notice that these pseudo Gini coefficients are defined relative to expression (11.10): the gross income ranking is used as the exogenous characteristic. The relative correlation coefficients are defined in equation (11.18); the relative rank-weighted error term is defined in equation (11.19). Applying equation (11.8) to the two problems in equation (11.11) gives: (11.20a) G. = OR,,GV + zRzGz + OJR?Gz+ ... + o,,R,G, by equation (11.16) and (11.20b) G. = 0-RI-'Glw+ O-R-G- + ... + .pRpGp+ (n-+ 1)A/n by equations (11.17) and (11.19). It now is possible to solve for G, and obtain:

(11.21a) Gy = (A+ - A- + E)/R,, where (11.21b) A+ = 0"R-'Gw + OwRWG2w+ ... + oRwGpw 0, [income effect] COMPUTATION PROCEDURE 383

(11.21c) A- = OIR'G++ O ±+R .. + 6'R'GŽ > O, and

[payment effect]

(11.21d) E = (n + 1)A/no,

= [(n + 1)/n]Q(ji6 + j262 + ... + jb)/9y by equation (11.19)

E(n + 1) /n] ( ial + j2 8 2 + .. + j. ) [decompositionerror] by equation (11.14). The inequality of net family income [Gd] is therefore decomposed into an income effect [A+], a payment effect [A-], and an error term [E]. When an income component is positively correlated with gross income-that is, when R7 > 0-an unequal distribution of an income component, indicated by a large G[, contributes to income inequality. When an income component is negatively correlated with gross income-that is, when RX' < 0-an unequal distribution of an income component contributes to income equality. The opposite relations are true for the payment effect. When a payment is negatively correlated with gross income, an unequal distribution of payment, indicated by a large GW,contributes to net income equality. The error term [E] tends to be small when net income accounts for a higher fraction of gross income and 0, is large.

Computation Procedure

A numerical example will now illustrate the computation procedure for the problem described in the preceding section. For the five families shown in table 11.1, there are two types of income (wage and property), two types of payment (tax and transfer), and an error term. Net income [Yj] and gross income [Xi] are also given. All families are arranged in a monotonically increasing order according to gross income, thereby satisfying expression (11.10). The pseudo Gini coefficients are computed relative to this family ranking. It should be noted in this example that the rankings 384 APPLICATIONS AND EXTENSIONS OF THE MODELS OF DECOMPOSITION

Table 11.1. Numerical Example of Original Income Data

Nota- Family Family Family Family Family Variable tion 1 2 5 4 5 Total

Wage income Wl 8 4 12 20 6 50 Property income W2 0 10 5 15 45 75 Tax payment Zi -1 -3 0 -4 -7 -15 Transfer payment Z2 -2 -2 -2 -2 -2 -10 Error term Si 0 1 0 1 -2 0

Net family income Yi 5 10 15 30 40 100 Gross family income Xi 8 15 17 36 49 125

Source:Constructed by the authors.

Table 11.2. Distributive Shares, Gini Coe.ticients, and Pseudo Gini Coefficients for Original Data in Table 11.1

Nota- 2 Variable tion X Y WI JV Z' Z

Mean 25 20 10 15 3 2 Distributiveshare in X oi 1.0 0.8 0.4 0.6 0.12 0.08 Distributiveshare in Y os - 1.0 0.5 0.75 0.15 0.10 Gini coefficient Gi 0.3296 0.3600 0.3040 0.5333 0.4533 0.0000 PseudoGini coefficient (G, - 0.3600 0.0960 0.5066 0.3467 0.0000 Relativecorrelation R, - 1.0000 0.3158 0.9499 0.7648 0.0000

- Not applicable. Source:Calculated from table 11.1.

of families according to X and Y are the same. This relation nevertheless is just an accident leading to R, = 1. Thus table 11.1 contains all the primary data needed for the decomposition problem. The computation procedure is set forth in tables 11.2 and 11.3. COMPUTATION PROCEDURE 885

Table 11.3. Decomposition Analysis of Original Data in Table 11.1

Nota- Variable tion Computation Value

Rank-weighted error term A = o/X = (jib + 1282 + *

+ j 5 b 5 )/X = -(4/15)/25 = -4/3 Income effecta A+ = ,wR,wG,w+ 2wRwGw= 0.4279

Payment effectb A- = OVRjGf+± ORG1 = 0.0519 Decomposition errorc E = (n + 1)A/noy = -0.0160 Decomposition analysisd Gy = A+ - A + E = 0.4279 - 0.0519 - 0.0160 = 0.3600

Relative weight 1 = A+/Gy - A-/GI + E/Gy = 1.1886 - 0.1446 + (-0.0440) 1.0000

Sources: Calculated from tables 11.1 and 11.2. a. See equation (11.20b). b. See equation (11.20c). c. See equation (11.20d). d. See equation (11.20a). CHAPTER 12

RegressionAnalysis, HomogeneousGroups, and Aggregation Error

THREE ADDITIONAL SUBJECTS require elaboration. The first is the manner in which regression analysis of variations in family income can be related to the analysis of additive factor components. The second is the analysis of the distribution of income by homogeneous groups of income recipients. The analysis of these groups could be so construed that the Gini coefficient is decomposed into intergroup and intragroup effects, as well as a crossover effect. That crossover effect will be shown to increase as the decisiveness with which ordinal rankings of groups affect earning power is perverted. The third subject is the error introduced when grouped data on the distribution of family income must be used because of the unavail- ability of primary data. It will be shown that the use of grouped data leads to the consistent underestimation of the index of inequality and hence the degree of that inequality.

Regression Analysis

One of the most popular methods used in attempts to explain the variation of family income is based on a linear regression model of the following form: 2 (12.1a) Y = a + b1X' + b2X ± ... + bqXg + a, where (12.1b) Xi > 0.

886 REGRESSION ANALYSIS 387

The family income is to be explained by independent variables [Xi] which stand for various ordinal characteristics, such as education, age, and sex. The term 6 represents a randomly distributed error term. The basic aim of regression analysis is twofold: first, to estimate the regression constant a and the regression coefficients bi; second, to assess the reliability of these estimations once the observable data of n families are given:

(12.2a) Y = col(Y1, Y2 , .... , ); (12.2b) Xi = col(Xfi,X,..., X,) > 0; (i = 1, 2, ... ,q)

(12.2c) 0 < yl < Y2 < ... < Yn. The total incomes of the n families and the values of the independent variables are shown as column vectors. Assume that the regression constant a and the coefficientsbi are already estimated and given as a starting point of the analysis-that is, the reliability of estimation, which is the focal point of traditional regression analysis, is not a concern. Once the values of equation (12.2) and the regression coefficientsare given: 2 (12.3a) Y = a, + b6X1 + b2X + ... + b,Xq + 6,, where (12.3b) a, = col(a, a, . . ., a),

(12.3c) 6, = col(61, 62, . . . , 6,), and

(12.3d) 61+ ±2 + *. . + 6. = 0, and where bi is an error term defined to ensure equality for the regression equation of the ith family. Notice in equation (12.3d) that the sum of all values of 6i is zero. It can now be seen that the vector of total family income is the sum of q + 2 components: the first component is the constant term a; the last component is the error term b6;the other q components are the independent variables.

Causationof G,,based on regressionanalysis Traditional regression analysis emphasizes the causes of variation in family income [Y]; it is not concerned with the cause of variation in the inequality of family income [G,]. Nevertheless, when the traditional regression analysis is done, it is possible to proceed with an analysis of G, based on the technique developed in chapter eleven for factor component analysis. This possibility is seen from 388 REGRESSION ANALYSIS equation (12.3a), where the Y vector is the additive sum of q + 2 column vectors: that is, Y now has q + 2 components. In particular, equation (12.3d) shows that equation (11.9) is applicable. Consequently the decomposition result obtained in equation (11.18) can be applied. The sign of the column vector biXi is the same as that of the regression coefficient. The sign of the column vector a. is the same as that of the regression constant. Therefore equation (12.3) can be rewritten in two ways, depending upon whether a. is positive or negative: 2 (12.4a) Y = a, + b1X' + b2X + .... + b,XP 2 - (cIZ' + c 2Z + ... + cqZ) + B. when a, > 0, and 2 (12.4b) Y = b1X1 + b2X + ... + bpXp

2 - (a + CIZ + C2Z + ... + CZq) + 6, when a, < 0, where: (12.4c) bi 2 °, (i = 1, 2, . ,p) (12.4d) ei < O, (i = 1, 2, . ,q)

(12.4e) Y = col(Yi, Y2, . . , Yn) 2 0, (12.4f) Xi= col(Xii, . x) > 0,

(12.4g) Z = col(Zi, Z2, ... , Zi) 2 0, (12.4h) a,= col(a, a,..., a), and

(12.4i) 6,= col(61, 62, .. , 6,) where

(12.4j) 61+ 62+ ±+ =. O. Use the notation M(X) to denote the mean of the column vector X. Applying this notation to the column vectors of equations (12.4a) and (12.4b) gives:

2 (12.5a) M(Y) = [a + b1M(XI) + b2M (X ) + ,.. + bpM(XP)]

2 - [cIM(Z') + c2 M(Z ) + ... ± c'M(Zq)] when a > 0, REGRESSION ANALYSIS 389

1 2 (12.5b) M(Y) = [b,M(X ) + b2M(X ) + ... + b,M(XP)] 2 - Ea + ciM(ZI) + c2M(Z ) + ... + cqM(ZQ) when a < 0,

(12.5c) = | a I /M(Y), (12.5d) = bjM(Xi)/M(Y), and (i = 1, 2, , p)

(12.5e) = ciM(Z) /M(Y) (i = 1, 2, , q) For the case when a > 0 define:

(12.6a) U = col(Ul, U2, , Un) q p = Y + ciZi = a,+ biXi + i=l i-1 by equation (12.4a),

(12.6b) U = Ui/n i=l

= Y + CiZli + CZ2 +± + CqZQ =a+ big, + b22 + .. + bpXp, and

(12.6c) X,= YI/U. For the case when a < 0 define:

(12.7a) U = col(Ul, U2, ... , Un) 2 = Y+a+cCZI+c 2 Z ±+.. CZq 1 2 = bX + b2 X + + b,XP,

(12.7b) U = E Ut/n

=Y+ a + 1C 1 + C2Z2 + .. +cqZ,

= b1X1 + b2X2 + + b±Xp, and (12.7c) = fY/U. The definition of the column vector U corresponds to equations (11.9c) and (11.9d). Its components, given by (Ul, U2, ... , U.), are assumed to be arranged in a monotonically increasing order as 390 REGRESSION ANALYSIS in expression (11.10):

(12.8) U1 < U2 < ... < U,. All the pseudo Gini coefficients are defined relative to this ranking. Respectively use the notation G(X) and G(X) to denote the Gini coefficient and the pseudo Gini coefficient, and define: (12.9a) G, G(Y), (12.9b) G(a.) = 0,

(12.9c) G(biXi) = G(Xi) = Gi, (i = 1, 2, ... ,p)

(12.9d) G(ciZi) = G!; (i = 1, 2, . . ., q) (12.10a) G, = G(Y), (12.10b) 0(a,) = 0,

(12.10c) G(biXi) = 0Q, (i = 1, 2, ... , p) (12.10d) G(ciZi) = GZ.; (i = 1, 2, . ,q)

(12.11a) R, = (12.11b) 4= G/GtI (i =1, 2, ,p) (12.11c) 4= G'/0i; and (i =1, 2, ... ,q)

(12.12a) E = [(n + 1)/n](jibi +±j22 ... + jnan)/Y, where (12.12b) ji = 2i/n(n + 1). Notice in equations (12.9) and (12.10) that the Gini coefficient and pseudo Gini coefficient for the column vector a, obviously are zero. The Gini coefficient and pseudo Gini coefficient for the column vector biXi obviously are the same as G(Xi); those for the column vector ciZi, the same as G(Zi). Hence the regression constant a and the regression coefficients bi and ci are not involved in the foregoing definitions. They nevertheless are involved in the definition of the relative shares in equation (12.5c). A direct application of equation (11.18) leads to:

(12.13a) G. = (A+ - A- + E) /R, where R, is defined as in equation (12.11) and where:

(12.13b) A+ = OftRGtx + OW2R + ... ± -RG (12.13c) A = 0lzRGz + RzGz + ... + 4RG,z and

(12.13d) E = [(n + 1)/n](j51 + j1262+ ... + j.6.) Y. REGRESSION ANALYSIS S91

Table 12.1. Numerical Example of Income Data and Regression Terms

Nota- Family Family Family Family Family Variable tion 1 2 5 4 5 Total Mean

Independent variables Xl¾ 4 2 6 10 3 25 5 XI 0 2 1 3 9 15 3 zli 1 3 0 4 7 15 3 Net family income Yi 5 10 15 30 40 100 20 Column vectors a= -2 a -2 -2 -2 -2 -2 -10 -2 bi = 2 b1xi' 8 4 12 20 6 50 10 b2 = 5 b,xl 0 10 5 15 45 75 15 cl = -1 clzl -1 -3 0 -4 -7 -15 -3 Estimated net family income Yi 5 9 15 29 42 - - Error term ai 0 1 0 1 -2 0 0 Gross family income Ui 8 15 17 36 49 125 25

- Not applicable. Source: Constructed by the authors.

The terms in equations (12.13b) and (12.13c) were defined in equations (12.5c) and (12.11); those in equation (12.13d), in equations (12.6), (12.7), and (12.12).

Computation procedure Table 12.1 gives for five families the family income EYi] and the values of the three independent variables EX', X2, and Z']. From this set of data a regression equation of the following form is estimated:

(12.14a) Y = a + b1Xl + b2X2 + c1Z1', where

(12.14b) a = -2, b1 = 2, b2 = 5, c1 = -1. 392 REGRESSION ANALYSIS

Table 12.2. Distributive Shares, Gini Coefficients, and Pseudo Gini Coefficients for Original Data in Table 12.1

ANota-

Variable tion a Xi X 2 Z1 Y U Net family income weight [YC/U] -- 4/5 Distributive share in Y oi -2/20 1/2 3/4 -3/20 1/1 Gini coefficient Gi 0.0000 0.3040 0.5333 0.4533 0.3600 0.3296 Pseudo Gini coefficient St 0.0000 0.0960 0.5066 0.3467 0.3600 - Relative correlation Ri 0.0000 0.3158 0.9499 0.7648 1.0000 -

- Not applicable. Source: Calculated from table 12.1.

When the values of Xl, X2, and ZV in table 12.1 are substituted into this equation, the column vectors a, b1xz, b2x2i, and c1x' are obtained. The sum of those vectors is the estimated value of net family income EY[J. The error term is the difference between Yi and Yi. Notice that the sum of the vector 8 is zero. Notice also that the vectors a and cix. are both negative. The sum of nonnegative vectors-that is, b1xl., b2,x2, and ai-is shown in the row for gross family income. The computation of pseudo Gini coefficients is carried out relative to this ranking (table 12.2). Notice that when the regression analysis is transformed into an income components problem, it takes on exactly the same numerical value as shown in table 11.2. Thus the decomposition analysis shown in table 12.3 merely is a repetition of that in table 11.3.

Remarks on chapter four The analysis of inequality of family wage income in chapter four was based on the decomposition equation (12.13a) In table 4.6 of that chapter the regression coefficients a,, a2, as, and a4 are positive; the regression constant ao is negative. This is a special case of equa- 2 tion (12.4b) in which the terms Z', Z , .. ., Z" vanish. Equation (12.7) reduces to the special case:

(12.15a) U =col (U1 , U2, . . . , U,,)

= Y + a. = b1X, + b2X2 + b3X3 + b4X4 + 5,; REGRESSION ANALYSIS 393

Table 12.3. DecompositionAnalysis of Original Data in Table 12.1

Variable Computation Value

Rank-weighted

error term =/Y= (ji+i + J2 62 + + j5b6/Y = (-4/15)/20 -1/75

Income effecta A+ = PR,Gl + VRl2G2= 0.4279 Payment effectb A- = OiRiGl + OnRIG. = -0.0519 Decomposition error0 E = (n + !)A/n = -0.0160 Decomposition analysisd G, = A+ - A + E = 0.4279 - 0.0519 - 0.0160 = 0.3600 Relative weight 1 = A+/G -A-I/G, + E/IG = 1.1886 - 0.1446 + (-0.0440) = 1.0000

Sources: Calculated from tables 12.1 and 12.2. a. See equation (12.13b). b. See equation (12.13c). e. See equation (12.13d). d. See equation (12.13a).

(12.15b) U1 < U2 < ... < U. implies that Y, < Y2 < ... < Yn by expression (12.8); (12.15c) R, = 1 as Gv = G, in equation (12.11a); (12.1.5d) , = Y/U = Y/(Y + a) in equation (12.7). Thus equation (12.13) reduces to the special case:

(12.16a) Gv = (1R1 Gi + 0 2R2G2 + ... + 0,R,G, + E, where

(12.16b) E = ((n + 1)/n) (j161 + j262 + . . . + j.8)/YI. Equation (12.16a) is the decomposition equation (4.3) in chapter four. In that chapter 4i is defined in equation (4.11e), Gl in equation (4.5b), Ri in equation (4.13a), and E = A in equation (4.12a). 394 HOMOGENEOUS GROUPS

In equation (4.18a) W is defined as the sum of the nonnegative components indicated on the right-hand side. Thus the decomposition equation (4.15) used in chapter four is the exact decomposition equation (10.5) of chapter ten.

Family Income Inequality with Homogeneous Groups

In the analysis of family income distribution, one popular approach is to identify homogeneous groups of income recipients. For example, the homogeneous groups in the urban sector may be capitalist families, blue-collar labor families, white-collar labor families, and civil servant families. For another example, the homogeneous groups in the rural sector may be landlord families, owner-cultivator families, and tenant families. When such groupings of families are accepted, the total family income of n families can immediately be classified into q mutually exclusive groups:

(12.17a) Xi = col(Xi, X2, .. ., Xin); (i 1, 2, . . ., q)

(12.17b) ni + n2 + . . + n,, = n; (12.17c) oi = ni/n; (i = 1, 2, ,q) (12.17d) Si = X + X ... + X+i; (i = 1, 2, ... ,q) (12.17e) XS, = Sl + S2 + + S,;

(12.17f) Xi =Silni; (i = 1, 2, ... , q) (12.17g) oi = Sls/v; (i = 1, 2, . ,q)

(12.17h) 01 + 02 + . . . + 0, = 1. In equation (12.17c) 9i is the fraction of families in the ith group; in equation (12.17g) Xs is the fraction of total income earned by the ith group. The average income in the ith group is given by XS in equation (12.17f). The value of Xi may be thought of as the income earned by a typical member of the ith group. Equation (12.17a) thus contains the primary data of this section.

Intuitive ideas associatedwith homogeneousgroups When a classification of families is given, the presumption is that the characteristic of each grouping is decisive in affecting total family income. More precisely two ideas are implied. FAMILY INCOME INEQUALITY WITH HOMOGENEOUS GROUPS 895

First, there is the presumption that the groups are ordinally ranked by their income-earning potential. Thus the q groups will be arranged so that:

(12.18) X1 < X2 < ... _ that is, typical incomes of the members of q groups are arranged in monotonically increasing order. As a further illustration of this point, suppose the n families to be cross-classified into six groups by education and sex (table 12.4). The integers in the six cells in this table indicate a particular ordinal ranking in which the lowly educated female contributes least in determining family income and the highly educated male contributes most. Altogether there are 720 (6!) possible ways to rank these cells ordinally. Ideally the acceptance of a particular ordinal ranking is the result of theorizing and constitutes a null hypothesis. In fact, the theorizing is informal, and the empirical ranking obtained in equation (12.18) thus is often taken to be indicative of the relative earning potential of the various groups. Second, such a group ordering, when given as in expression (12.18), is decisive in two senses. One sense is that the variation of income within each group-that is, the variation of family income within each cell in table 12.4-should not be as great as the variation of income between the groups. Therefore the notions of intragroup and intergroup variation in incomes must be separated. The other sense is that no member of a group should receive an income higher than any member of a group with a higher ranking. When perversity is observed, it is to be regarded as evidence contradicting the hypothesis that groupings are decisive in affecting income. As an illustration of this idea, suppose in an apartheid society that the ordinal

Table 12.4. Numerical Example of the Classification of Families by Education

Ordinal rank Low Medium High Sex education education education

Female 1 2 3 Male 4 5 6

Source: Constructed by the authors. 896 HOMOGENEOUS GROUPS ranking of white and nonwhite groups may be so decisive that no member of the nonwhite group receives an income higher than even the poorest member of the white group. If perversity of order is observed, the apartheid system will be regarded as incomplete. It follows that to measure this decisiveness a "crossover effect" should somehow be measured. In summary, once family income is classified into homogeneous groups as in equation (12.17), an intergroup variation [Gr], an intragroup variation [A], and a crossover effect [C] should be defined.

Intergroup variation The natural definition of Gr, the intergroup variation, is the Gini coefficient for the following set of n numbers:

nl n2

(12.19a) R = COI(XI, XZ, . ,. . X1; X 2, X2, . . .X2; n,,

***;X9,X,Z , XQ);

(12.19b) S,, = niXl + flX 2 ± ... + n,,Xq. Equation (12.19a) is constructed by replacing every XJ by the mean of the group [iV] to which it belongs. It is apparent in this set that there is no intragroup variation, because all families within each group receive a typical income. If the groups indeed are ho- mnogeneous and all members within each group cannot be distinguished from each other by their income, then equation (12.19a) represents the income pattern of idealized homogeneous groups. To define the Gini coefficient for this set, first define the following numbers:

(12.20) Ci = ni + n2 + ... + ni; C, = 0. (i = 1, 2, ... ,q) where Ci is the cumulative number of families earning a typical income less than or equal to Xi. The next theorem indicates the method of computing the Gini coefficient for the pattern of idealized homogeneous groups indicated by R in equation (12.19a):

THEOREM 12.1. Gr = G(R) = [0 1(Co + C1 - n)/n]

+ [E2(C 1 + C 2 - n)/n]

+ . .. *+ E,(C_j + Cq-n)/n] FAMILY INCOME INEQUALITY WITH HOMOGENEOUS GROUPS S97

Proof: Theorem 8.2 gives:

Gr= (Xi - X>)niny/S,n for i > j

= g1X1/Svn + g2X2 /S,n + ... + ggXq/Sv,n, where

gi = [ -(Ci-(n - C)]ni. The reason for this result is that Xi appears Ci-, times as the upper end in the definition of income gaps and n - Ci times as the lower end in the definition of income gaps. Thus:

G, = E (Ci_- + Ci - n)niXi/S,n = E (Ci- + Ci -n)i/n.

This completes the proof.

Intragroup variation and the crossover effect In defining the intragroup variation [A] it is to be noted because there are q groups that A is by nature a weighted average of the intragroup variations of q groups. Therefore the intragroup variation can be heuristically defined as:

(12.21a) A = OlklGl + 02,2G2 + ... + 6q4,GQ, where

(12.21b) Gi = G(Xi). (i = 1, 2, . , q)q.

The intragroup effect [A] is defined to be the weighted average of the Gini coefficients of the q groups, where the weights are the product of the relative group size [Di] and the relative income share [0.,] respectively defined in equations (12.17c) and (12.17g). To define the crossover effect [C] it will first be assumed that the incomes of families within each group are arranged in a monotonically nondecreasing order:

(12.22) X1 < X2 < ... < Xn. (i = 1, 2, **q) Each of the n families so ordered will be assigned a natural ranking (1, 2, . .. , n). In other words, each family will be assigned a lexicographic ranking in the following way:

(12.23) The rank of Xt is Ci-1 + j (lexicographic rank). (j = 1, 2, . ,ni) (i = 1, 2, .. q) 398 HOMOGENEOUS GROUPS

This ranking can be illustrated by an example with seven families and three groups:

(12.24a) (Xl = I < Xl = 3; X1 = I < X2 = 4 < Xs = 7;

X1 = 6 < X2 = 10);

(12.24b) (1, 2; 3, 4, 5; 6, 7);

(12.24c) X1 = 2 < X2 = 4 < X3 = 8. Thus the families in each group are arranged in a monotonically nondecreasing order, satisfying expression (12.22). Furthermore it can be seen from expression (12.24c) that the group means are also arranged in a monotonically nondecreasing order, thereby satisfying equation (12.18). The ranks assigned according to expression (12.23) are indicated in expression (12.24b). In order words, after the families are arranged in a lexicographic order, expression (12.23) simply is the first n integers arranged in the natural order. The ranking may be referred to as a lexicographic ranking conforming to the group decisiveness. The main idea is that members of the first group are ranked first, those of the second group second, and so on. When the lexicographic ranking of expression (12.23) takes the place of the characteristic rank [C] of equation (9.1) in chapter nine, the Gini coefficient [G] of n families is the sum of two terms, s+ and s-, according to equation (9.18a). In this case the s+ term is the average of the gaps that support the lexicographic ordering; the s- term is the average of the gaps that contradict the lexicographic ordering. In the numerical example s- is calculated as follows:

S-= [(X1- X) + (X3 - X1)]/(7 X 32)

- [(3 - 1) + (7 - 6)]/224 = 3/224.

Notice because of expression (12.23) that a term in s- can only occur between two members belonging to different groups. Further- more such a term exists when and only when a member of a lower income group earns more income than a member of a higher income group, thus perverting the lexicographic ranking. The s- term may therefore be referred to as the crossover effect. Formally the cross- FAMILY INCOME INEQUALITY WITH HOMOGENEOUS GROUPS 399 over effect can be defined as:

(12.25) s- = E (Xl- Xi) for all X' > Xi with i < j.

Decomposition of G, When the primary data on homogeneous groups are given as in equation (12.17), the intergroup variation [Gr], the intragroup variation [A], and the crossover effect Es-] can be defined. Now let G, be the Gini coefficient for the n numbers X, in equation (12.17a). The basic theorem to be proved is:

THEOREM 12.2. GV= G, + A + 2s-.

The theorem states that the Gini coefficient EG,] can be decomposed into an intergroup variation term EGr]J an intragroup variation term [A], and twice the crossover effect [2s]--.1 All these terms are nonnegative. As a result, if homogeneous groups are postulated, the Gini coefficient of all families, when approximated by intergroup and intragroup effects, always leaves a nonnegative error 2s-]. The magnitude of this error term is determined by the degree to which group decisiveness is perverted. Theorem 12.2 can be illustrated by the numerical example in equation (12.24a) and tables 12.5 and 12.6, which classify the income of seven families into three homogeneous groups. The means of the three groups are arranged in a monotonically increasing order. With the lexicographic ordering, the supporting and nonsupporting gaps are shown by s+ and s-. The decomposition of G, according to theorem 12.2 is given in the bottom row. To prove theorem 12.2 all that is needed is to prove the following lemma:

LEMMA 12.1. G s+ - s- = A + G,.

1. This three-way decomposition of the Gini coefficient to address the problem of homogeneous groups was first proved by Bhattacharya and Mahalanobis. It was rediscovered by Rao and reinterpreted, with simplified proofs, by Pyatt. Mangahas presented a two-way decomposition corresponding to intragroup and intergroup effects alone. In chapter five we worked with the variance, not the Gini coefficient, primarily because of the simplification caused by the disap- pearance of the GI term for the particular problems tackled there. For the sources of studies mentioned here see note 1 to the introduction of part two. 400 HOMOGENEOIUS GROUPS

Table 12.5. Numerical Example of the Classification of Seven Families into Three HomogeneousGroups

Nota- GroupI Group8 Groups 2 Variable tion [xI] [z ] [XI] Total

Family income x, 1,3 1,4,7 6,10 - Group frequency ni 2 3 2 7 Group income xi 4 12 16 32 Mean of group income xi 2 4 8 7/32

Relative group frequency Oi 2/7 3/7 2/7 - Group income share Oi 1/8 3/8 4/8 - Group Gini coefficient G1 1/4 1/3 1/8 -

- Not applicable. Source:Constructed by the authors.

By using equation (9.15a) in addition to lemma 12.1, theorem 12.2 can be immediately derived. To prove this lemma, the Gini coefficients for every one of the q homogeneousgroups are defined as:

(12.26a) Gi = G(Xi) = G(X' < X2 < ... < Xn_ )

= (2/ni)ui - (ni + 1)/ni, where (i = 1, 2, ... , q)

(12.26b) ui = (1) (X /Si) + (2) (X'/Si) + ... + (ni) (Xni/Si) by theorem 8.1. The pseudo Gini coefficient (G0) takes on the following form:

(12.27a) G, = (2/n) - (n + 1)/n, where

(12.27b) 4t = OIUI + 102U2 + ... + OqUq + C1 02 + C2 03 + ... + Cq1i4q, where Ci is defined as in equation (12.20).

q n; Proof: By theorem8.3 and letting S, = E X,: i-I j-I FAMILY INCOME INEQUALITY WITH HOMOGENEOUS GROUPS 401

Table 12.6. Decomposition Analysis of Data in Table 12.5

Variable Computation Value

Intergroup variation G, = (Xi- Xj)n,nj/Svn = (4 - 2)(2)(3) + (8 - 2)(2)(2) + (8 - 4)(2)(3) = 230/112 Intragroup variation A = aiGi = (2/7)(1/8)(1/4) + (3/7) (3/8) (1/3) ± (2/7)(4/8)(1/8) = 9/112 Crossover effect s- = (X' - X') + (X' - XI)/(32)(7) = 3/224 Supporting gap s+ = (2+12+4+3+6+1+4+5+9 +3+7+5+9+2+6+3)/ (32)(7)= 81/224 Pseudo Gini coefficient G= A + G, = S+-S- = 30/112 + 9/112 = 81/224 - 3/224 = 39/112 Gini coefficient G, = S+ + S- = 81/224 ± 3/224 = 84/224 = 21/56 Decomposition of Gini coefficient Gv = A + G, + 2S- = 9/112 + 30/112 + 3/224 = 84/224 = 21/56

Source: Calculated from table 12.5.

ews n2 n, UV= ,, iXi/Sy± + (C1 i)X2il/S + .+ . + X (Cq-_+i)Xy/& i=l ~i-I i-I >;l n2 = , i(X'/S 1 )0 1 + E (C1 + i) (X2%/S2 ) 2 + * i=l ~~~~i=l nq + X (Cq-i + i) (X./Sq)oq i=l

- lU± + 02U2+ .+ . + 0Uq + C12 + C243 + ... ±Cq-ic0. This completes the proof of equation (12.27b). 402 HOMOGENEOUS GROUPS

Substituting equation (12.27b) into equation (12.27a) gives: 2 G,( (flul± + 2U2 + .. + quq)

2 + - (C1I 2 + C203 + ... + Cq,q5q)- (n + 1)/n

Oini [2 Xu_nl + 11 02r2 [ 2-n2 + 1

n ni ni j n Ln2 n2

+ [ + nq2 2 11 X + ]] n nn n

+ 12 + . + n] +[1n n ... n

_ 01 I + ,n + .+ ,,n n n n

2 + - [(Cl0,2 + C203 +. + Cqi4)q)] n

=1A1G,+ 2 .22G. + Oq9qGq+ B, where

B nn2-n n n2 + 2C,-n n3 + 2C2-n n n n

+n, + 2C,- - n

± n+(n,- n) + 02(C, + C2 - n) + 03(C2 + C3 - n) +

+ 4)q(Cq-_i+ Cq -n)]/n

- Gr by equation (12.26). Hence:

0, = A + G, by equation (12.21). This completes the proof of lemma 12.1, which also proves theorem 12.2. GINI ERROR ARISING FROM THE USE OF GROUPED DATA 403

Gini Error Arising from the Use of Grouped Data

One important problem relevant to the analysis in this volume was first brought to our attention by Professor Orcutt. As an illustration of that problem, which is associated with the use of grouped data on the distribution of family income, assume that an income survey has been conducted for ten families and that the results are processed as follows: (12.28a) (4, 10, 14, 5, 12, 15, 6, 14, 16, 4) [survey returns] (12.28b) (4, 4, 5, 6, 10, 12, 14, 14, 15, 16) [ordered tabulation of primary data] (12.28c) [(4), (4, 5, 6), (10, 12, 14), (14, 15, 16)] [partitioned primary data] (12.28d) Faamily group

Variable 1 2 3 4

Number of families 1 3 3 3 Total income 4 15 36 45 Mean income 4 5 12 15

[published frequency distribution]

(12.28e) [(4), (5, 5, 5), (12, 12, 12), (15, 15, 15)]

[grouped data] The survey returns are first ordered into a tabulation: that is, they are computerized. Next some partitioning of the ordered tabulation is selected. In the example here the ten families are classified into four 404 AGGREGATION ERROR groups according to total income rank. In actual practice a decile partition is often chosen to enable international comparisons. Then a frequency distribution is computed. The frequency distribution presented here indicates the number of families, total income, and average income for each family group. In reality the number of families usually is very large, and the final tabulation of the frequency distribution is the only practical way in which data can be published and made available to the general user. When the original survey returns (12.28a) are processed into a frequency distribution, all intragroup variations are suppressed. Published data almost always suppress intragroup variations when the sample size is large. One method a researcher can use to recover part of the suppressed information for empirical work is by interpolation-that is, by guessing or speculating about the intragroup variations with the aid of additional assumptions.2 An ideal method, which we strongly advocate, obviously is to work with primary data-something which is becoming increasingly feasible in this age of computerization, but which was not possible for us.3 The purpose in this section, however, is to investigate the seriousness of this suppression when the published frequency distribution is used to calculate the Gini coefficient. The problem is not serious when grouped data are used for the computation of mean income. In grouped data every member belonging to the same group is interpreted as having the same income as the mean income of the group; those mean values essentially replace the primary data.4 Suppose the incomes within each group to be randomly distributed around the group mean. Then the average income computed from grouped data will not differ much from the true mean of the primary data. But if grouped data are used to

2. Joseph L. Gastwirth, "The Estimation of the Lorenz Curve and Gini Index," The Review of Economics and Statistics, vol. 54, no. 3 (August 1972), pp. 306-16. 3. This method is especially advocated for any future research that involves the multidimensional cross-listing of data. Our work in chapter four has shown that the most serious deficiency of published data is the absence of cross-listing, not the suppression of intragroup variation. Consequently this section, as well as the interpolation method, may some day have only historical interest in the analysis of the distribution of family income. 4. This obviously is the only interpretation when the original survey data are not available and interpolations are not used. GROUPING ERROR IN THE ANALYSIS OF ADDITIVE COMPONENTS 405

compute the Gini coefficient, or for that matter any reasonable index of inequality, there will always be an underestimation of the degree of inequality. In the numerical example the true Gini coefficient computed from primary data is: (12.29a) G7 = 0.256; the Gini coefficient computed from grouped data is: (12.29b) G, = 0.240. Thus G, underestimates GT by 0.016. By comparing the grouped data and primary data it is seen that GQ, when computed from grouped data, captures only the intergroup effect of G'. Because the grouped data represent a consecutive partitioning of a monotonically increasing vector, there is no crossover effect in this case. Equation (12.21a) can be used to compute the intragroup effect in the numerical example as follows:

(12.30a) 01 = 0.1, 02 = 0.3, Os= 0.3, 04 = 0.3;

(12.30b) (A = 0.04, 02 = 0.15, 03 = 0.36, 4= 0.45;

(12.30c) GI = 0, G2 = 4/45, G3 = 2/27, G4 = 4/135; (12.30d) A = (0.1) (0.04)0 + (0.3) (0.15) (4/45) ± (0.3) (0.36) (2/27) + (0.03) (0.45) (4/135) = 0.016. That value of A is exactly the amount of underestimation. Thus, when grouped data are used, there always is a systematic downward bias in the estimation of the true degree of inequality.

Grouping Error in the Analysis of Additive Factor Components

When the pattern of total income has factor components, the use of grouped data presents additional problems, which can be illustrated by the numerical example in table 12.7. The total income [Yi], wage income [Wi], and property income [Eri] of six families constitute the primary ungrouped data for this example. Notice that Yi is the sum of Wi and 1ri. Furthermore, as in the tabulation discussed at the beginning of the preceding section, the primary ungrouped 406 AGGREGATION ERROR

Table 12.7. Numerical Example of the Factor Gini Error in Grouped Data

Primary ungroupeddata Wage income pattern in (f = 1)a publisheddata Total family Wage Property Family income income income f = 2 f = 3 f = 6

1 Y 1= 12 10= w1 2 = 7r, 8 25.3 19.2 2 Y2 = 14 6 = w 2 8= r2 8 25.3 19.2 3 Y 3 = 64 60= w3 4= r3 30 25.3 19.2

4 Y 4 = 70 0 = W 4 70 = T4 30 13.3 19.2 5 Y6 = 80 0 = w5 80 = 7r5 20 13.3 19.2 6 Ye = 100 40 = W6 60 = r6 20 13.3 19.2

Source: Constructed by the authors. a. The symbol f stands for the number of families in each income class. b. Of the type used for the model of additive factor components in this volume.

data for the six families are ranked according to total income:

Y1 < Y2 < Y 3 < Y 4 < Y5 < Y6. As a result, the primary data on wage income [Wj] and property income [ri] are not monotonically ranked. If the primary data are available, the values of Wi can be monotonically ranked, as in table 12.7, and used to compute the true wage Gini [GT(W)]. The same holds for the values of ri. The published data available to the general reader do not, however, include the primary ungrouped data. According to the standard practice of data publication, some integer f is always chosen so that primary data are consecutively partitioned into classes of families and that f families are included in each income class. In the example here, f is a divisor of 6: f = 1, f = 2, f = 3, and f = 6. The primary data on wage income in table 12.7 correspond to the case f = 1. The cases f = 2, f = 3, and f = 6 correspond to different levels of aggregation of wage income patterns and are also given in table 12.7. Notice the difference between patterns based on published data, which are monotonically ordered by total income rank, and those based on primary data, which are monotonically ordered by GROUPING ERROR IN THE ANALYSIS OF ADDITIVE COMPONENTS 407

Wage income patterns based Property income pattern on original unpublished basedon original data and ranked by Published groupeddatab unpublished data and wagerank (f = 2) ranked by property rank Prop- Total Wage erty f = 1 f = 2 f = 3 f = 6 income income income f = I f = 2 f = 3 f = 6

0 0 2.0 19.2 13 8 5 2 3 4.6 37.3 0 0 2.0 19.2 13 8 5 4 3 4.6 37.3 6 8 2.0 19.2 67 30 37 8 34 4.6 37.3 10 8 36.6 19.2 67 30 37 60 34 70.0 37.3 40 50 36.6 19.2 90 20 70 70 75 70.0 37.3 60 50 36.6 19.2 90 20 70 80 75 70.0 37.3

wage income rank. At each level of aggregation the group mean replaces the income of a particular family. The numerical example's published data on total income [Yi], wage income EWiJ, and property income [?ri] are grouped for f = 2 in table 12.7. Notice that total income is the sum of wage income and property income. In other words, the published grouped data satisfy the basic requirement of the additive factor-components problem: Yi = Wi + 1ri. The published data in this grouped form customarily are available only for a limited number of values of f-usually for 15 to 25 family groups. In the early chapters of this book, such as chapter three, the decomposition analysis is based on the use of grouped data in this form: following the decile convention, the value of f is equal to the total number of families divided by ten. Thus, when primary ungrouped data are not available on tape, researchers must use grouped data at a particular level of aggregation corresponding to a particular value of f. The true wage Gini and the pseudo wage Gini can be computed from the primary data in table 12.7: G,(W) = 0.61; Gt(W) = 0.09. Based on different levels of aggregation, a set of wage Ginis [G (W, f)] and a set of pseudo wage Ginis [E(W, f)] can also be computed. Notice that G,(W) = G(W, 1) and L,(W) = G(W, 1) . In figure 12.1 408 AGGREGATION ERROR

Figure 12.1. Behaviorof Indexes of Inequality under Different Levels of Aggregation

0.8 G(W,1) = 0.61 0.7 - G(W,2). = 0.58 0.6 A A 0.5- (W,s). = 0.41 0.4 _ -G(W,2) = 0.25

0.2 _G(W,1) = 0.09 - G(W,S) = 0.14 0.1- B - ____B 1 4 - -- -0.1 __ /5 6 -0.2- G(W,2) = 0.14 4 -0.3 _ d(wa) = -o_i G(W,6) = G(W,6) 0 -0.4

True wage Gini a- a' True pseudo wage Gini b- b' - Wage Gini for wage pattern ranked by total income rank - - -Pseudo wage Gini for wage pattern ranked by total income rank Wage Gini for ------wage pattern ranked by wage rank

Source: Calculated from table 12.7. the values of the true wage Gini [G( W, 1) ] and the true pseudo wage Gini EG(W, 1)] are respectively indicated by the horizontal lines aa' and bb'. The values of the wage Ginis at different levels of aggregation are: G(W, 2) = 0.25; G(W, 3) = 0.14; and G(W, 6) = 0. The corresponding values of the pseudo wage Ginis are: G(W, 2) = 0.14; G(W, 3) = -0.17; and G(W, 6) = 0. As the data become more aggregated-that is, as the values of f become higher-G(W, f) decreases. Thus G(W, f) implies an increasing underestimation of the true wage Gini as f increases from one. That underestimation is indicated by the vertical gap, G,(W, 1) - G(W, f), between the solid curve and the horizontal line aa'. Notice that the pseudo Gini [EG(W,f) ] behaves more erratically as f increases. When the wage pattern is monotonically ranked, a different set of wage Ginis can be computed: G(W, 1)" = 0.61; G(W, 2)m = 0.58; G(W, 3)m = 0.41; and G(W, 6),,, = 0. These values are indicated in figure 12.1. Notice in this monotonic case that the underestimation of GROUPING ERROR IN THE ANALYSIS OF ADDITIVE COMPONENTS 409 the true wage Gini represents the intragroup effect discussed in conjunction with equations (12.29) and (12.30) . By comparing the two error terms, it can be seen that G(W, 1) - O(W, f)m generally is smaller than G(W, 1) - G(W, f) for every f. The reason is that the wage patterns associated with the second error are not monotonically ranked. Thus, in addition to the intragroup effect, there are other sources of underestimation. It should now be clear that two distinct problems, both associated with the Gini error, arise from the use of grouped data. The first problem is related to the size of the Gini error when the income pattern is monotonically arranged. It has been shown that this error [G(W, 1) - G(W, f) m ] corresponds to the intragroup effect, which can be calculated when the primary ungrouped data are available.6 When the primary data are not available, this error can be estimated by an interpolation method which has already been developed.7 The second problem is conceptually more complicated. It is associated with the Gini error [G(W, 1) - G(W, f) ] when a factor income component is not monotonically ranked. Our discussion should have made it clear that this constitutes a special problem which arises when the grouped data are used for the analysis of additive factor components-that is, when the arrangement of factor incomes is by total income rank and for this reason is not monotonic. For this new problem the Gini error is larger than the intragroup effect, but its precise nature remains to be investigated from a

5. Exchangeswith Graham Pyatt of the World Bank indicate that two additional words of clarificationmay help to avoid further confusion.First, if only published groupeddata are available,as often is the case, the values of G(W, f)m> cannot be computed. Second, G(W, f)m is irrelevant to the additive factor- componentsmethod of Gini decomposition.This is true despite the fact that G(W, f)m is a better approximation of the true wage Gini than is G(W, f) for each value of f. The reason is that the patterns of wage and property income must add up to the pattern of total income, as is illustrated by the published data in table 12.7,if this method is to be applied. But when wage and property income respectivelyare monotonicallyranked according to wage and property rank, the patterns of factor incomedo not add up to the pattern of total income. 6. Of course, it is preferable to use primary data, when available, and thus avoid this error. The interpretation of this error neverthelessis conceptually important. 7. See Gastwirth, "The Estimation of the LorenzCurve and Gini Index." 410 AGGREGATION ERROR theoretical standpoint. 8 Thus the intrinsic interpretation of the error term, as a property of the primary ungrouped data, remains to be studied. Furthermore no method has yet been developed, at least to our knowledge, to estimate upper and lower bounds of this error when primary data are not available-that is, a method cormparable to the interpolation method for the simple case when the income pattern is monotonically arranged. This second problem is serious for all users who must rely, as we have in this volume, on published grouped data to implement the additive factor-components approach. Future research can be expected to proceed along three fronts: theoretical research on the nature of the Gini error as a property of ungrouped data; empirical research using ungrouped data to determine the seriousness of underestimation associated with each level of aggregation9 ; the design of interpolation methods when primary data are not available. The empirical results in this volume will no doubt require reassessment as further work in these areas comes to fruition.

8. For certain special cases it can be shown that the Gini error has two components: an intragroup effect and a crossovereffect. See theorem 12.2. 9. The purpose of that research ultimately is to determine safe levels of aggregation Ef] so that the error falls within tolerable limits. Index

Additive expenditure components, 264, of, 57, 95n, 128; and reallocation 291. See also Consumption expendi- effect, 18, 113-16; and rural by- ture; Direct tax payments; Educa- employment, 114, 249-51, 315; as tion; Food and clothing expenditure; type one or type two income, 74, 89, Housing expenditure; Indirect tax 94-95, 98, 104 payments; Savings Agriculture, 3; in colonial Taiwan, 22, Additive factor components. See Addi- 24-26; diversification of, 47; em- tive factor income components pirical findings and policy conclu- Additive factor components model, 7, sions for, 312-17; fixed capital in, 48; 18, 19, 133, 324, 373, 376-78; data and industry, 24-26, 27, 37; infra- requirements of, 10; and earnings- structure in, 45-46; labor force in, function technique, 139; and linear 31, 113, 114; and nonagricultural regression equations, 203, 211, 214- income, 115; population in, 46; in 15, 326, 386-94. See also Decomposi- postcolonial Taiwan, 28, 31, 46-50; tion formulas production in, 225, 226. See also Additive factor Gini decomposition, 18. Agricultural income; Farm families; See also Decomposition formulas Land reform; Rural households; Additive factor income components, Rural family income; Rural industry 7-8, 73n, 224, 291; and decomposi- Agricultural production. See Agri- tion formulas, 14, 326, 351-57; and culture grouped data, 14; grouping error, All households, 87, 90, 94-95, 98, 99, 405-10; and growth theory, 376-78 100, 102-04, 128, 312; Gini coeffi- Adelman, Irma, 2, 35 cient for, 99, 100, 108-12. See also Age, as labor attribute, 130, 132-37, Rural households; Urban households 142-43, 145, 317, 320; and analytical Analysis, methods of, 17-20 cross-listing of data, 200; and wage- Approximation: equation, 83; of factor rate inequality, 161, 164-66, 170, components, 367-69; methods of, 171, 175-76, 179-80. See also Family 326, 367-72 attributes Assets, 6-7; capital, 5; distribution of, Agricultural income, 12, 49, 54, 56, 74, 41-44, 50-53; human, 6-7, 225; in- 87, 90; distributive share of, 57, 88, dustrial, 37; labor, 6-7; physical, 98, 113-16; empirical findings and 6-7, 225; structure of, 89 policy conclusions for, 314-15; as Atkinson, Anthony B., 15n, 325n factor component, 7; and FID, 98, Atkinson index, 6 104, 126; factor Gini effect and, 18, Attributes. See Family attributes; 88, 102, 103, 106, 127; Gini coefficient Labor attributes

411 412 INDEX

Average contradicting gap, 342-46 Consumer price index (cPi), 34n Average supporting gap, 342-46 Consumption expenditure, 267, 269- 70, 273-76, 278 Consumption goods, imports of, 53 Consumption structures, 264-65, 267 399nt Consumption taxes, 19. See also Taxes, 399n . ~~~~~~~taxation Bias of innovation. See Labor-usin taxtio bias of innovation g Contradicting gap, average, 342-46 hris of i o Council on U.S. Aid, 51n Bureauil 65BdeadSaisis9 Credit cooperatives, rural, 22-23, 45 Bureau of Budget and Statistics, 194 Crossover effect, 386, 398-99 By-employment, rural, 114, 249-Si, Cyclical noise, 34n

Dalton, Hugh, ln Cannan, Edwin, ln Data: analytical cross-listing of, 199- Capital: control of, 25; as factor income 201, 202, 203; computerized, 14; component, 83; fixed, 48; foreign, 28, DGBAS, 10-13, 54, 56, 65n, 90, 113, 45, 311; working, 48. See also Capi- 115, 131n, 193n, 194n, 234, 255n, tal-labor ratio; Industrial assets 267-72, 294; on family expenditure, Capital accumulation, 85n 267-72, 290; grouped, 14, 403-10; Capital assets, 5 interpretation of, 14-15; primary, Capital deepening, 84-85, 86, 108, 11-12, 194, 199-201, 202, 403-10; 120, 317 published, 11-12, 13, 131n, 404-10, Capital goods, imports of, 53 409n; quality of, 11-13, 65n; scarcity Capital intensity, 52, 118n, 119 of, 54, 69; and underestimation of Capital-labor ratio, 84, 86-87, 11i8n Gini coefficient, 65n; ungrouped, 14, Chang, Kowie, iOn, 38n-39n, 54n 403-10; unpublished, 131n, 403-10 Characteristic ranks, 340-42 Data aggregation, 13-14. See also Chen Chao-Chen, 38n Grouping error Chenery, Hollis, 112n Decile groups, 13, 65n, 90n Cheng Chen, 40n Decomposition analysis, 11, 69, 126, China, mainland, 26 211n, 291, 325. See also Decomposi- Classical economists, 1, 4 tion formulas; Gini coefficient analy- Cline, William R., 128n sis; Gini coefficient(s) Coefficient of variation, 6 Decomposition formulas, 8, 14, 17, 73, Colonial infrastructure, 37 74, 75, 79, 89, 100, 132, 146, 159; and Colonial Taiwan, 21-26, 37, 316 additive factor income components, Commercialization, 84, 86. See also In- 14, 326, 351-67; derivation of, 325- dustry, industrialization; Modern- 26, 351-72; exact computation pro- ization cedure for, 359-60; of family income Commodity tax, 265 after tax, 270-79; for homogeneous Computerized data, 14 groups, 9, 327, 394-402; of income in- Consolidation error, 11 equality, 73, 75-83; and linear Consolidation issue, 13. See also model, 326, 363-65, 373, 374; and Grouping error monotonic model, 326, 365-66, 373, Conspicuous consumption, 266, 269, 375-76; sectoral, 226-31; for house- 271, 276 holds, 87 Consumer behavior, 275, 291 Deficit financing, 26 INDEX 413

Degree of overestimation, 77-78, 97 181, 183, 184-91, 200, 317, 318-19, Demographic factors, and FID, 249-63 320-21. See also Family attributes Dependency theorists, 128 Elasticity of substitution, 84 Descending homogeneous case, 183, Employment. See By-employment; 190-92 Labor; Labor force; Underemploy- Deterministic theory, 20, 291-92 ment; Unemployment Development theory, 3, 7, 18, 84, Error of estimation, 77-78 323-24 Error, nonlinearity, 83, 98, 99 DGBAS.See Directorate-General of Bud- Error term, 97, 211n; rank-weighted, get, Accounting, and Statistics 146, 161 Diaz-Alejandro, Carlos F., 53n Estimator Gini coefficient, 77, 79 Direct tax burden, 264, 265, 267, 269, Europe, Western, 4 271, 279, 283-89, 290 Exact decomposition computation pro- Direct taxes, taxation, 19, 279, 286, cedure, 359-60 287, 290, 322-23. See also Taxes, Exchange rates, 27, 29 taxation Expenditure. See Consumption ex- Directorate-General of Budget, Ac- penditure; Family expenditure; counting, and Statistics (DGBAS): Housing expenditure data of, 10-13, 54, 56, 65n, 90, 113, Export-led industrial expansion, 29 115, 131n, 193n, 194, 234, 255n, 267- Export ratio, 31 72, 294 Exports, 30-31, 32, 53 Disaggregate analysis, 5 Export substitution. See Primary ex- Discrimination. See Wage-rate in- port substitution; Secondary export equality substitution Distributive shares, 54n, 75, 77, 87-88; of agricultural income, 57, 88, 98, 113-16; of factor income components, 75, 83-84; of nonagricultural Factor Gini coefficients, 8, 72, 82, income, 66-67, 88; of property in- 83, 357-59; and factor Gini effect, come, 87, 88; of wage income, 84, 120-26; of property income, 82, 86, 87, 88 120-26; of wage income, 82, 120-26; Distributive weights. See Distributive weighted, 77 shares Factor Gini curves, 98 Diversification index, 50 Factor Gini effect, 18, 74, 83, 313; and Domestic markets, 28-29 agricultural income, 18, 88, 102, 103, 106, 127; and FID, 86-87, 126-29; and factor Gini coefficients, 120-26; and Earnings-function technique, 138-39, Gini coefficients, 99-100, 102, 105, 214-15 106, 107, 108; and nonagricultural Economic Planning Council, 48n, 54, income, 125-26, 127; and property 64n, 199, 294n income, 18 Economic policies, development of, and Factor income components, 4-5, 7, 17, Taiwan findings, 308-24 54, 75; distributive shares of, 75, 83, Education, 309-10; of family head, and 84; Gini coefficient of, 55, 56-57, 80- FID, 240-43; family expenditure for, 81; and growth and FID, 72-129; in- 19, 264, 265, 267-68, 273, 276-78; dex of inequality of, 72, 74; labor government expenditure for, 290; as and capital as, 83; linear approxima- labor attribute, 130, 132-37, 139, tion of, 367-69; negative, 326, 380- 142-43, 145, 161, 162, 163-65, 170, 83; with observation error, 326, 378- 414 INDEX

80; and total income inequality, 73; and family ownership, 18; rules of, rank index of, 77; types of, 72-73 140. See also Family size and com- Factor income distribution, 89 position Factor income inequality, 75-83 Family grouping, 55n Factor income pattern, 98n Family head, attributes of, and sectoral Factor-price ratio, 118n decomposition equation, 235, 240-43 Factor prices, 1, 4, 30 Family income. See Family distribution Factor shares, 1, 4, 90 of income; Family wage income; Net Family affiliation, 130, 139. See also family income; Property income; Family attributes Total family income; Wage income Family attributes: and inequality of Family income inequality: empirical family income, 19, 224-26, 255; and findings and policy conclusions for, sectoral decomposition equation, 312-17; and savings and consump- 231, 235-40. See also Age; Education; tion, 265; and taxation, 266, 267, Sex 279-89, 321-23. See also Family dis- Family consumption patterns, 19. See tribution of income also Consumption expenditure; Family income structure, 264-65 Family expenditure Family influence, 318, 319. See also Family distribution of income (FID), Family affiliation 1-3, 4, 5, 6, 34-35, 100-01, 312; and Family investment in physical and demographic factors, 249-63; as human resources, 265, 267, 268, 270, descriptive device, 1; and DGBAS 271, 276-78 data, 90-99; and education of family Family lineage, lln head, 240-43; empirical findings and Family size and composition: and total policy conclusions for, 310, 312, 314, wage income, 131; and wage-rate in- 315, 316, 317; and factor Gini effect, equality, 180-93, 226, 249, 254-56 86-87, 126-29; and factor income Family type, 201, 203 components, 72-129; and functional Family savings. See Savings distribution effect, 18, 86, 98, 99-100, Family wage income, 4-5, 130-223; and 103, 106, 107, 108, 116-20, 126-29, differentiation of labor force, 130-38, 313-14, 316-17, and functional dis- 141-46; empirical findings and policy tribution of income, 67, 89, 312; conclusions for, 317-21; and family growth and, 7, 17, 18, 72-129; and affiliation, 130, 139; and family form- land reform, 38, 44, 50; overall, 65- ation, 130, 139, 168-93, 224-26; and 71; and primary import substitution, industrialization, 130; sectoral and 38, 71, 84, 310-11, 317; and realloca- locational dimensions of, 224-63. See tion effect, 88-89, 99-100, 103, 105, also Wage income 108, 126-29, 313-15; rural, 12-13, Family-weight effect, 225, 231, 243, 54-64, 66, 110, 114, 128, 312; sectoral 245, 247 and locational dimensions of, 224- Family welfare, 265, 289-91 63; and taxation, 19, 272-78, 279-89; Farm sector, 233-34, 245-46. See also urban, 12-13, 64-65, 107-08, 110, Agriculture; Rural industry 127-28, 312, 313, 314, 316. See also Farmers' associations, 22, 23, 39, 45, Net income, Property income; Total 253 family income; Wage income Farm families, 19; changing size and Family expenditure, 19, 264, 267-307 composition of, 254-56; DGBAs defini- Family farm size, 54, 55n tion of, 201-02; distribution in Family formation, 309; and distribu- colonial Taiwan, 23; income gap be- tion of wage income, 131, 168-93; tween nonfarm families and, 225, INDEX 415

243, 245, 254; reduction in tax bur- technique for, 126, 325, 342-43; and den of, 253-54; rise of nonfarm factor Gini effect, 99-100, 102, 105, income of, 112-16; and rural by- 106, 107, 108; of factor income com- employment, 249-51; and sectoral ponents, 55, 56-57, 80-81; graphic decomposition formula, 227-31. See summary of, 346-48; and homogen- also Rural households eous group decomposition, 227n Farm rents, 39-40 under linear transformation, 361-63; Farm size and multiple cropping, 56 of nonagricultural income, 88; pat- Fei, John C. H., 3n, 73n, 84n, 85n, 99n, tern of, over time, 108-09; of prop- 109n erty income, 98, 119, 120-26; for Female(s); heads of households, 235; rural households, 99, 101, 108-12, and wage-rate inequality, 131, 136, 120;sectoral, 109-12, 121; semiurban, 143, 145, 161-62, 166, 170, 171, 175; 112; after tax, 279; before tax, 279; workers, 134-35 and time patterns, 123; of total in- FID. See Family distribution of income come, 54n, 55-56, 72, 81, 98, 100, First-stage import substitution. See 103, 108, 109; underestimation of, Primary import substitution 65n; for urban households, 64-65, Fixed capital, 48 99, 101, 108-12; of wage income, Food and clothing expenditure, 264, 64-65, 98, 119, 120-26 273. See also Consumption ex- Government expenditure on health, penditure education, and family welfare, 289- Food processing industry, 37 90, 322n Foreign aid, U.S., 28, 45, 311 Gross domestic product (GDP), 43 Foreign capital, 28, 45, 311 Gross national product (GNP), 99, 289 Foreign trade, 17 Grouped data, 14. See also Grouping Functional distribution effect, 18, 74, error 83, 85, 88, 313; and FID equity, 86, Grouping error, 326-27, 386, 403-10 98, 99-100, 103, 106, 107, 108, 116- Growth path, labor-intensive, 67, 127, 20, 126-29, 313-14, 316-17; and 249-51, 309, 310. See also Labor- property income, 313, 316; and urban using bias of innovation households, 107-08, 313-14, 316-17 Growth theory, 89, 120, 376-78 Functional distribution of income, 1, 12, 44, 67, 89, 127, 312 Functional specialization, 57 Handicraft sector, 25, 115 Hayami, Yujiro, 49n Gastwirth, Joseph L., 14, 404n, 409n Head of household, characteristics. See Gini coefficient analysis, methodology, Family head 325-410 Health, government expenditure on, Gini coefficient(s), 6, 8, 12-15, 18, 35- 290, 322n 36, 37, 54n, 65, 69, 82; additive fac- Hicks, John R., 84n tor property of, 8; of agricultural Hicksian labor-using bias of innova- income, 57, 95n, 120-26; for all tion, 84, 85, 86, 108, 120, 253, 317 households, 99, 100, 108-12; al- Hidden taxes, 253, 290n ternative definitions of, 326, 328-34; Historical perspective, 3-4 as average fractional gap, 331-34; Ho, Samuel P. S., 22n, 38n, 4 1n, 43n, causative factors of changes in, 99- 45n, 50n, 51n 116; comparative magnitudes of total Homogeneous case, descending, 183, and sectoral, 109-12; decomposition 190-92 416 INDEX

Homogeneous group decomposition, 9, Industry, 28, 110, 226; and agriculture, 327, 394-402; and Gini coefficient, 24-26, 27, 37; and changes in income 227n inequality, 243-49; in colonial Homogeneous labor groups, 150-55 Taiwan, 24-26, 37; decentralized, Household surveys. See All households; 112, 249, 315-16, 317; and differen- Data; Rural households; Semiurban tiation of labor force, 130-31, 177; households; Urban households and distribution of assets, 50-53; Housing expenditure, 263, 267, 270-71, export-led expansion of, 29; private, 273-76, 278, 323 50, 52; publicly owned, 50-52; and Hsieh, S. C., 1On sex discrimination, 318-19; urban, Hsing Mo-huan, 109, 115n 119, 120, 122-23, 124, 128, 316. See Hsu Wen-fu, 45n also Labor-using bias of innovation; Human assets, 225 Rural industry Human capital, 5, 19, 129 Inflation, 26, 34n Innovation-intensity effect, 84, 86. See also Labor-using bias of innovation Imperial examination system, 321 Interest rates, 29 Import licensing, 27 Intergroup inequality effect, 9, 19, 386, Imports, 53 396-97 Import substitution. See Primary im- International Labour Organisation port substitution; Secondary import (ILO), 114n substitution Intersectoral effect: and decomposition Income. See Agricultural income; formula, 225-31; for degree of urban- Family distribution of income; ization, 246-49; for farm and non- Family wage income; Functional dis- farm sectors, 245-46. See also Func- tribution of income; Nonagricultural tional distribution effect income; Property income; Total Intersectoral income inequality, 1IOn family income; Transfer income; Intersectoral payments, 90 Wage income Intragroup inequality effect, 9, 13, 19, Income classes, 13 326, 386, 397-98 Income components. See Factor income Intrasectoral effect: and decomposition components formula, 225-31; for degree of urban- Income-disparity effect, 225, 231, 245, ization, 246-49; for farm and non- 247, 248, 255 farm sectors, 245-46 Income fractions, 328, 340-42 Intrasectoral income inequality, 1iOn Income gap, farm-nonfarm, 225, 243, Intrasectoral structural dualism, 125 245, 254 Investment patterns, family, 265, 267, Income ranks, 340-42 268, 270, 271, 276-78 Income-relative, 226, 243 Income shares, relative, 121, 122 Income sources, classification of, 351. See also Income Jacoby, Neil H., 29n Indexes of inequality, 6-9 Jain, Shail, 13n Indirect taxes, taxation, 19, 279, 286, Japan, colonial legacy in Taiwan, 21- 287, 290, 293-94, 322-23. See also 26, 37, 316 Taxes, taxation JCCR. See Joint Commission on Rnral Indirect tax burden, 264, 265, 267, Reconstruction 269-70, 271, 279, 285-89, 290, 294 Joint Commission on Rural Recon- Industrial assets, 37 struction (JCCR): data, 10, 45-46, 54, Industrial exports, 30, 53 61, 62n, 114 INDEX 417

Job location, as labor attribute, 132, 113, 114; rural, 161-68; stratifica- 136-38, 143-45, 159, 160, 161; and tion of, 5, 7, 18; urban, 161-68. See analytical cross-listing of data, 201 also Labor Labor-intensive industries, 67, 116, 118, 119, 120 Labor-using bias of innovation, Hick- Kaohsiung City, 63 sian, 84, 85, 86, 108, 120, 253, 317 Kirby, Edward S., 15n Lai, W. H., 49 Kuo, Shirley W. Y., 12n, 73n, 113n Land reform, 37, 38-46, 249, 252-53,

Koo, Anthony J. C., 40n 312, 314 Kuzoets,Anton, 2. 3n,4n5 99, 112, 128, Land-to-the-tiller program, 39, 52. See 224, 226, 227n, 243, 255n also and reform Kuznets effect, 6, 86, 99, 104, 109, 112, Latin America, 3n 127, 151 Least-squares method, ordinary, 78n LDC. See Less developed countries Less developed countries (LDc), 2, 4, 5-6, 127 Labor: absorption of, 28, 31, 74, 85, Lee, T. H., 44n 86n, 251, 317; as factor income com- Leontief inverse matrix, 293 ponent, 83; family ownership of, 18, Lewis, W. Arthur, 35, 99, 112, 120, 128 87, 225; male and female, 115; Life-cycle income, lln mobility of, 224; pricing of, 130; re- Linear approximations, 78, 367-69 allocation of, 17, 32, 47, 57, 74, 113- Linearity error, 369-70 16, 225, 312; scarcity of, 32, 34, 109, Linearity specification, 98n 316-17; surplus of, 17, 31-32, 108- Linear model, decomposition formula, 09, 312, 316-17; unskilled, 30, 34. 326, 363-65, 373, 374 See also Labor force; Wage-rate in- Linear regression equation, 141, 146, equality; Wage rates 326, 386-94 Labor assets, 6 Linear regression lines, 79, 81 Labor attributes: impact on wage rates, Linear regression method, 90, 131, 138, 131, 132, 133, 135, 136-37, 138, 141- 324 46, 160-68, 318-21; and pattern of Liu, Paul K. C., 50n wage income of individual workers, Liu, S. F., 50n 139. See also Age; Education; Labor Lorenz curve, 1, 328-30 characteristic Gini; Labor charac- Lu, Kuang, 39n teristic weight; Labor correlation characteristic; Quality characteristics; Sex Labor characteristic Gini, 146-55, 158, Mahalanobis, B., 73n, 325n, 333n, 399n 159 Malthus, Thomas, 4 Labor characteristic weight, 147, 155- Mangahas, Mahar, 73n, 325n, 399n 57, 159 Manufacturing, 24-25, 37, 52, 67, 119. Labor correlation characteristic, 147, See also Industry; Labor-using bias 157-68, 169, 171 of innovation; Nonagricultural pro- Labor force: agricultural, 31, 113, 114; duction differentiation of, 5, 72, 122, 130-38, Marginal labor force, 175, 177, 320 141-46, 146-68; family ownership of, Market mechanism, government inter- 7; formation of modern, 18; homo- ference with, 314 geneous, 150, 153, 155; marginal, Markets, domestic, 28-29 175, 177, 320; nonagricultural, 31, Marxist theorists, 128 418 INDEX

Meerman, Jacob, 322n 56. See also All households; Urban Mehran, F., 73n households Mexico, 65 Nonfarm Gini coefficient, 112 Migration, 340n Nonlinearity error, 83, 98, 99 Mincer, Jacob, 138n Nonlinearity term, 82 Minimum progressiveness, 282-83, Nonuniform homogeneous case, 183, 286n 190 Modernization, 110-11, 115, 122-23, No-reversal-of-rank condition, 282, 283 130-31, 137, 177. See also Industry, industrialization Monotonic model, decomposition for- Occupation, as labor attribute, 132; mula, 326, 365-66, 373, 375-76 and analytical cross-listing of data, Morris, Cynthia Taft, 2, 35 201 Multiple-cropping index, 50, 56-57 Overestimation, degree of, 77-78, 97 Multiple regression analysis, 141. See also Linear regression method Paauw, Douglas S., 3n Paukert, Felix, 2 National income, decomposition of, 75, Personal income, total, 65n. See also 231-43 Total family income Negative rank correlation, 77n Philippines, 115n, 316 Nepotism, 7, 309 Physical assets, and pattern of family Nepotism coefficient, 142, 145 ownership, 7, 225 Net domestic product (NDP), 47-48, 52 Physical capital, 5; family investment Net factor Gini effect, 102 in, 19; heterogeneity of, 129 Net family income, 266, 272-78. See Population growth, 131 also Taxes, taxation. Power generation, in colonial Taiwan, Net income structure, 266 25 Net supporting gap, 343-45 Primary data, 11-12, 194, 199-201, Nonagricultural factor Gini effect, 102, 202, 403-10 106, 125-26, 127 Primary export substitution, 17, 30-36, Nonagricultural income, 87, 98; dis- 53, 56, 63, 84, 113, 311, 322 tribution of, 66, 67; disaggregation Primary import substitution, 17, 26- of, 74; early forms of, 115; empirical 30, 32, 49, 52, 56, 67, 71, 84, 310-11, findings and policy conclusions for, 317 314-15; Gini coefficient of, 88; and Private industry, 50 rural by-employment, 114, 249-51, Private land, 40-41 315 Production complementarity, 85n, 86n Nonagricultural labor force, 31, 113, Production substitutability, 85n, 86n 114 Progressive taxes, taxation, 271, 282, Nonagricultural production, 28, 37, 283, 288, 322-23 112, 225, 226; and ratio of wage Property income, 4, 7, 56, 72, 73, 74, 75, share to property share, 116 81, 83, 87, 264; analytical cross-list- Nonfarm sector, 233-34, 245-46 ing of data on, 199; distributive Nonfarm employment, 61-62 shares of, 87, 88; as factor compo- Nonfarm families, 19; income gap be- nent, 7; factor Gini coefficient of, 82, tween farm and, 225, 243, 245, 254; 120-26; and factor Gini effect, 18; and sectoral decomposition formula, and functional distribution effect, 227-31; size and composition of, 254- 313, 316; Gini coefficient of, 98, 119, INDEX 419

120-26; rank correlation between Regressive taxes, taxation, 271, 282, total income and, 77; rural, 54, 56, 283, 285, 322-23 113; sectoral Gini coefficient of, 121; Relative factor prices, 30 as type one income, 73, 82, 90; as Relative income shares, 121, 122 type two income, 90n Relative share ratio, 116 Pseudo factor Ginis, 352-57 Ricardo, David, 4 Pseudo Gini coefficient, 158n, 326, 328; Rice, hidden tax on, 253 graphic summary of, 346-48; and Rosen, Sherwin, 139n pseudo Lorenz curve, 328, 334-37 Rural by-employment, 114, 249-51, Pseudo Lorenz curve, 334-37 315 Public lands, 39, 40. See also Land Rural credit cooperatives, 22, 23, 45 reform Rural dualism, 122. See also Structural Publicly owned industry, 50-52 dualism Published data, 11-12, 13, 131n, 404- Rural families. See Family distribution 10, 409n of income; Farm families; Rural Pyatt, Graham, 73n, 325n, 339n, 340n, households 349n, 399n, 409n Rural households, 4, 12-13, 87, 90, 94, 97, 99, 101, 105, 106, 128; agricultural income and, 314, 315; and FID, Quality characteristics, 326, 338-50 12-13, 54-64, 66, 110, 114, 128, 224, Qualty carateritics32, 33-50 312; Gini coefficient for, 99, 101, 108-12, 120; income sources of, 87; nonagricultural income of, 112-16, Ranis, Gustav, 73n, 84n, 85n, 99n, 314, 315; and reallocation effect, 105- lO9n 06, 313; and reallocation of labor, Rank correlations, 77 313-14; spatially dispersed, 12-13; Rank index of factor income compo- surveys of, 10-11. See also Farm nents, 77 families; Sectoral decomposition Rank-weighted error term, 146, 161 equation Rao, V. M., 73n, 325n, 399n Rural industry, 50, 61-63, 113, 114, Raw materials, imports of, 53 115, 116, 118, 119, 120, 122, 125, 128, Reallocation effect, 74; and agricul- 315; decentralization of, 315-16, 317; tural income, 18, 113-16; and FID and property income, 54, 56, 113; equity, 88-89, 99-100, 103, 105, 108, and wage income, 54, 56, 57-61. See 126-29, 313-15; and rural house- also Industry; Labor-using bias of holds, 105-06, 313 innovation Reallocation of labor, 17, 32, 47, 57, 74, Rural unemployment, 50 113-16, 225, 312, 313-14 Rural workers. See Labor force; Job Real wages, 17, 32, 35, 36, 84, 85, 109, location 120, 312, 316, 317 Ruttan, Vernon W., 49n Redistribution. See Land reform; Re- allocation effect Regression coefficients, 78, 90, 142 Salary income, urban, 64-65. See also Regression constants, 78, 82, 90 Wage income Regression equation. See Linear re- Sales tax, 265 gression equations Savings, family, 19, 27, 264, 265, 267, Regression lines. See Linear regression 273, 276-78, 291 lines Savings rate, 28, 32-33 Regression relations, 78n Savings structure, 264, 265 420 INDEX

Secondary export substitution, 34. See Taiwan Pulp and Paper Corporation, also Primary export substitution 52 Secondary import substitution, 29, 34. Taiwan Sugar Corporation, 40 See also Primary import substitution Taxes, 5, 8, 19, 127, 279-89, 321-23; Second World War, 22, 23, 51 burden of, 264, 265, 267, 269, 271, Sectoral decomposition equation, 225- 279, 283-89, 290, 321-22; com- 31, 233-34 modity, 265, and consumption, 19; Sectoral property Gini, 123 direct, 19, 279, 286, 287, 290, 322-23; Sectoral Gini coefficients, 109-12, 121 and expenditure, 264-307, 321-23; Segmentation model, 9 and FID, 19, 279-89; hidden, 253, Semiurban Gini coefficient, 112 290n; indirect, 19, 279, 286, 287, 290, Semiurban households, 110-11, 112 293-94, 322-23; progressive, 271, Sex, as labor attribute, 130, 132-34, 282, 283, 288, 322-23; reductions in, 135-36, 139, 142-45, 317-20; and 249, 253-54; regressive, 271, 282, analytical cross-listing of data, 200; 283, 285, 322-23; sales, 265 and wage-rate inequality, 7, 131, Tax payments structure, 264, 265, 266 136, 143, 145, 161-62, 166, 170, 171, Technology, 49, 312. See also Industry; 175, 235, 237, 309, 318, 319, 340n. Labor-using bias of innovation See also Family attributes Tenant farming, 24, 38-42 Share ratio, relative, 116 Terms of trade, 27 Smith, Adam, 4 Thailand, 115n, 316 Stable wage share, 67 Theil, Henri, 105n, 1iOn, 325n Structural dualism, 110, 122; intrasec- Theil index, 6, liOn toral, 125 Total family income, 7, 8, 18-19, 54, 58, Subphases of transition growth, 3, 4, 65n, 67, 73, 77; definition of, 72; dis- 17, 26. See also Primary export sub- aggregation of, 74; Gini coefficient stitution; Primary import substitu- of, 54n, 55-56, 72, 74, 81, 98, 100, tion; Secondary export substitution; 103, 108, 109; and factor income Secondary import substitution; inequality, 75-83; index of inequal- Turning point ity of, 72, 74; ranking of, 55n; rank Sugar refining, 119 correlation between property income Supporting gap; average, 342-46; net, and, 77; and taxation and expendi- 343-45 ture, 8, 264-307; and wage rates, Surplus labor, 17, 31-32, 108-09, 312, 142, 145, 146, 161-62, 166-68; of 316-17 rural families, 113-16. See also Swamy, Subramanian, 227n Family distribution of income; Net family income; Wage income Total Gini curve, 98 Taipei City, 1ln, 63 Total income inequality, decomposition Taipei Provincial Government, Com- technique for, 75-83 mittee on the Census of Agriculture, Total income pattern, 72 114n Total personal income, 65n Taiwan, colonial, 21-26, 37, 316 Town workers. See Labor force Taiwan Agriculture and Forestry De- Transfer income, 72, 73, 75, 77, 78, 79, velopment Corporation, 52 81, 127, 264; and analytical cross- Taiwan Industrial and Mining Com- listing of data, 199; as type three pany, 52 income, 73, 97n Taiwan Province, lln Transition growth, subphases of, 3, 4, INDEX 421

17, 26. See also Primary export sub- Urbanization, 19, 226, 234-35, 243-49 stitution; Primary import substitu- Urban-rural model, 18 tion; Secondary export substitution; Utilities, 119 Secondary import substitution; Utopian socialism, 1 Turning point Tsui, Y. C., iOn Turning point, 84, 85, 86, 99-108, 109, Wage income, 18, 72, 73, 75, 78, 81, 83- 124, 125, 127, 243n, 311-12 84, 87, 130-223, 264, 309; analytical Type one income, 72-73, 74, 78-79, 80, cross-listing of data on, 199; and dif- 82, 89, 94-95, 104, 285n ferentiation of labor force, 130-31, Type three income, 73, 79, 80, 97 132-38, 144-46; distributive share of, Type two income, 72-73, 74, 78-79, 80, 84, 86, 87, 88; as factor component, 82, 89, 94-95, 98, 104, 285n 7, 72; factor Gini coefficient of, 82, 120-26; and family formation, 130- 31, 139, 168-93; and functional distribution effect, 313, 316; Gini co- Underemployment, 21, 50, 251. See also efficient of, 64-65, 98, 119, 120-26; Labor; Labor force of individual workers, 138, 139, 146- Unemployment, 251. See also Labor; 68, 318; and industrialization, 130; Labor force rural, 54, 57-60, 61-62, 113; sectoral Unemployment compensation, 290 Gini coefficient of, 121; as type two Ungrouped data, 14, 403-10 income, 73, 74, 90; urban, 64-65. Uniform homogeneous case; 183, 184- See also Real wages; Wage-rate 86, 188 inequality Uniform semihomogeneous case, 183, Wage income pattern, 7 186-88 Wage income weight, 171, 178-79 U.S. foreign aid, 28, 45, 311 Wage index, 133, 135 Unpublished data, 131n, 403-10 Wage-profit ratio, 188n Urban dualism, 110, 122, 123 Wage-rate inequality: age and, 161, Urban families. See Urban households 164-66, 170, 171, 175-76, 179-80; Urban family income. See Urban house- and family size and composition, holds, and FID 180-93, 226, 249, 254-56; sex and, 7, Urban Gini coefficient. See Gini coeffi- 131, 136, 143, 145, 161-62, 166, 170, cient of urban households 171, 175, 235, 237, 309, 318, 319, Urban households, 4, 12-13, 87, 90, 99, 340n 101, 107, 108, 128; capital and assets Wage rates, 131, 312; Gini coefficient of, 313; decomposition equation for, of, 146; and individual wage earners, 87; and FID, 12-13, 64-65, 107-08, 146-68; and labor heterogeneity, 131, 110, 127-28, 225, 312, 313, 314, 316; 132, 133, 135, 136-37, 138, 141-46, and functional distribution effect, 160-68, 318-21; regression coeffi- 107-08, 313-14, 316-17; Gini coefficients of, 138 cient for, 64-65, 99, 101, 108-12; in- Wage share, 67, 116, 120, 128 come sources of, 87; property in- Wage structure, 5, 18 come of, 316; spatially concentrated, Wang You-tsao, 49n 12-13; surveys of, 10-11; wage in- Wei, Yung, 252n come of, 316 Weighted factor Gini coefficient, 75, 77 Urban industry, industrialization, 119, Weighted income fractions, 328 120, 122-23, 124, 128, 316 Welfare, 177, 290 422 INDEX

Welfare income, 75, 79 Yale University, Economic Growth West Pakistan, 67 Center, 199 Women, and wage-rate inequality. See Yang, T. Martin, 43n Sex, and wage-rate inequality Yu, Y. H., 115n Working capital, 48 THE WORLD BANK AND THE YALE ECONOMIC GROWTH CENTER supported the research leading to the publication of this volume. Established as an activity of the Department of Economics in 1961, the Economic Growth Center is a research organization whose purpose is to analyze the economies of developing countries and their relations with economically advanced nations. Its current program of research is focused on six principal areas: basic processes of economic development; agriculture and rural development; technology choice and change; economic demography and labor markets; poverty, employment, and the distribution of income; and international economic interdependence, including North-South problems. Publi- cations of the Center include book-length studies and journal reprints by staff members. For more information, write to the Economic Growth Center, Box 1987, Yale Station, New Haven, Connecticut 06520, U.S.A. The full range of World Bank publications, both free and for sale, is described in the Catalog of World Bank Publications; the continuing research program is outlined in World Bank Research Program: Ab- stracts of Current Studies. Both booklets are updated annually; the most recent edition of each is available without charge from the Publi- cations Unit, World Bank, 1818 H Street, N.W., Washington, D.C. 20433, U.S.A.

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